Seminarios

Futuros Eventos

2017-10-20
16:00hrs.
Coloquio de Matemática UC
Matthieu Arfeux. Pucv
Polinomios Con Coeficientes Complejos y Sus Deformaciones Desde el Punto de Vista Dinámico
sala 2
Abstract:

Estudiar la dinámica de un polinomio complejo consiste simplemente en tratar de predecir lo que pasa cuando uno toma un número complejo y aplica de manera repetitiva esta misma función. Obviamente el comportamiento depende del valor inicial elegido. En esta charla comenzaremos por presentar rápidamente cómo clasificar esos comportamientos.

 

Después, nos podemos preguntar qué ocurre al tratar de cambiar de polinomio. En grado dos, por ejemplo, esta pregunta consiste en entender el famoso conjunto de Mandelbrot.

 

Finalmente, explicaremos que se entiende por “deformar” la dinámica, presentaremos ideas de algunos trabajos de William Thurston y Mary Rees que nos permitió, en conjunto con Jan Kiwi, demostrar una famosa conjetura de John Milnor de 25 años respeto a la dinámica de los polinomios complejos de grado tres.

2017-10-06
16hrs.
Coloquio de Matemática UC
Jorge Zanelli. Centro de Estudios Científicos (Cecs)
Tba
Sala 2
Abstract:
TBA
2017-09-28
17:00hrs.
Seminario de Teoría Espectral
Georgi Raikov. Facultad de Mateméticas, PUC
Teoría Espectral de Hamiltonianos Cuánticos. II
Sala 1
Abstract:
El propósito principal del ciclo de dos charlas "Teoría espectral de hamiltonianos cuánticos" del 21 y 28 de septiembre es despertar el interés de alumnos de licenciatura hacia los problemas matemáticos que aparecen en la teoría espectral de hamiltonianos cuánticos (operadores auto-adjuntos en espacios de Hilbert).

En la primera charla se presentarán algunos hechos básicos como el teorema espectral, la idea de cuantificación y las propiedades básicas de los operadores de Schrödinger, Pauli y Dirac.

En la segunda charla se hablará de temas más avanzados como hamiltonianos fibrados (por ejemplo, operadores con coeficientes periódicos) y hamiltonianos ergódicos.

Como ya indicado, el ciclo está orientado hacia alumnos de licenciatura pero puede ser interesante también para alumnos de postgrado y postdoctorados.
2017-09-26
10:00hrs.
Seminario General - Grupos de Trabajo
Luciano Sciaraffia. PUC Chile
Agujeros Negros, Flujos Geométricos y la Desigualdad de Penrose en Relatividad General.
Sala 3, PUC
Abstract:
Roger Penrose conjeturó que la masa total de un espacio-tiempo con agujeros negros debería estar acotada en términos del área de sus horizontes de sucesos. Un caso especial de esta desigualdad es la desigualdad Riemanniana de Penrose. Discutiremos apectos cualitativos de la masa en relatividad general y describiremos dos demostraciones de la desigualdad utilizando flujo de curvatura media inversa y flujo conforme de métricas.

Eventos Pasados

2017-09-22
10:00hrs.
Estadística Educacional
Gabriel Munoz Z.. Pontificia Universidad Católica de Chile
Un modelo estadístico en Estructuras de Conocimiento
Abstract:

En una formulación general de un modelo estadístico en una estructura de conocimiento, la probabilidad de un patrón de respuesta R depende de parámetros asociados tanto a los ítems como a una distribución de probabilidad p sobre la estructura de conocimiento. En esta charla se resumirá el trabajo titulado Finite Markov Learning Models for Knowledge Structures (Falmagne, 1994) dándole una estructura a p relacionando la formulación estadística con modelos tradicionales IRT haciendo énfasis en los problemas de identificación existentes.

Se comenzará dando las definiciones estándar de estructuras de conocimiento para luego presentar el modelo estadístico.


Sala 5 - Facultad de Matemáticas UClies.mat.uc.cl
2017-09-22
16hrs.
Coloquio de Matemática UC
Serge Richard. Nagoya University, Japan
C*-algebras in spectral and scattering theory
Abstract:
Since the early days of quantum mechanics, it has been admitted that physical observables correspond to self-adjoint elements in some operator algebras on Hilbert spaces. The precise concept of a C*-algebra has been introduced by Gelfand and Naimark in 1943, and since then the interaction between C*-algebras and quantum mechanics has been very fruitful. During this presentation, we shall review some of the results on spectral and scattering theory obtained during the last 20 years with C*-algebraic tools.
Sala 2
2017-09-22
14:30hrs.
Seminario de Geometría Algebraica
Natalia García . PUC Chile
El problema de los N cuadrados
Abstract:
El Problema de los N cuadrados (o Problema de Büchi) pregunta por el largo máximo de una sucesión de números enteros cuyos cuadrados tienen segundas diferencias iguales a dos. El largo máximo conocido de un ejemplo de estas sucesiones es cuatro.

En 2000, Paul Vojta estudio las curvas de género cero o uno de las superficies relacionadas a este problema, resolviendo este problema bajo la conjetura de Bombieri-Lang (es decir, que no puede haber sucesiones de este tipo de largo 8), y también su análogo para cuerpos de funciones de manera incondicional. El método para encontrar curvas de género bajo en una superficie que estamos estudiando en este seminario es inspirado en este trabajo de Vojta.

En esta charla, mostraremos con más detalles el sketch del método para encontrar todas las curvas de género bajo en una superficie, y estudiaremos como se aplica, paso a paso, al ejemplo del Problema de los N cuadrados (utilizaremos la noción de curva omega-integral, pero casi nada de teoría de haces). Si el tiempo lo permite, veremos que clase de hipótesis necesita un sistema de ecuaciones Diofantino para que éste método se pueda aplicar, con la idea de poder aplicar a futuro este método a otros problemas de teoría de números.
Sala 2http://www.mat.uc.cl/~urzua/
2017-09-22
17:15hrs.
Seminario de Pregrado en Matemáticas
Pablo Herrera. PUC
Tercer problema de Hilbert
Abstract:
El teorema de Bolyai-Gerwien dice que dados dos poligonos cuales quiera de la misma area es posible cortar uno de ellos en un número finito de piezas poligonales de forma que estas piezas puedan reordenarse formando exactamente el otro polígono. El tercer problema de hilbert consiste en preguntarse lo mismo pero para el caso de poliedros que poseen el mismo volumen cuya respuesta es que no siempre es posible.
Sala 2
2017-09-21
17:00hrs.
Seminario de Teoría Espectral
Georgi Raikov. Facultad de Matemáticas, PUC
Teoría espectral de hamiltonianos cuánticos. I
Abstract:
El propósito principal del ciclo de dos charlas "Teoría espectral de hamiltonianos cuánticos" del 21 y 28 de septiembre es despertar el interés de alumnos de licenciatura hacia los problemas matemáticos que aparecen en la teoría espectral de hamiltonianos cuánticos (operadores auto-adjuntos en espacios de Hilbert).

En la primera charla se presentarán algunos hechos básicos como el teorema espectral, la idea de cuantificación y las propiedades básicas de los operadores de Schrödinger, Pauli y Dirac.

En la segunda charla se hablará de temas más avanzados como hamiltonianos fibrados (por ejemplo, operadores con coeficientes periódicos) y hamiltonianos ergódicos.

Como ya indicado, el ciclo está orientado hacia alumnos de licenciatura pero puede ser interesante también para alumnos de postgrado y postdoctorados.
Sala 1
2017-09-21
17:00hrs.
Seminario de Postgrado en Matemáticas
Sebastián Burgos. Pontificia Universidad Católica de Chile
Análisis Multifractal de Promedios de Birkhoff
Abstract:

En el espacio simbólico se consideran dos potenciales Hölder. Se definen conjuntos de nivel de los promedios de Birkhoff hacia el futuro con un potencial y hacia el pasado con el otro. Queremos estudiar la función que codifica la descomposición del espacio en estos conjuntos de nivel: la función que manda dos números reales a la dimensión de Hausdorff del conjunto de nivel respectivo. El resultado principal es que los conjuntos de nivel son densos en el espacio, pero la función que los codifica es lo más regular posible, analítica real.


Sala 3
2017-09-20
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Giovanni Motta. Puc, Facultad de Matematicas, Departamento de Estadistica
Adaptive Estimation of Time Varying Covariances and Auto-Covariances
Auditorio San Agustinhttps://www.ing.pug.cl/ingenieria-matematica
2017-09-15
13:30hrs.
Seminario de Geometría Algebraica
Natalia García. PUC Chile
Curvas omega-integrales
Abstract:
En esta charla, vamos a definir lo que son las curvas omega-integrales. Estas curvas son fundamentales en el método para encontrar todas las curvas de género bajo en una superficie, y se pueden ver como un análogo algebraico de las curvas integrales de una ecuación diferencial.

Al comienzo, explicaremos las nociones necesarias de geometría algebraica para definir estas curvas, daremos la definición, y si el tiempo lo permite mostraremos un sketch del método para encontrar las curvas de género bajo en superficies.
sala 2
2017-09-15
15:00hrs.
Seminario de Geometría Algebraica
Eduardo Oregón. PUC Chile
Nilpotencia y Cociclos de Matrices
Abstract:
El Teorema de Caley-Hamilton nos dice que toda matriz satisface su propio polinomio característico. Esta restricción algebraica codifica información dinámica del proceso de iterar una matriz. En esta charla, obtendremos una restriccion algebraica similar, válida para un cociclo de matrices arbitrario. La herramienta fundamental para esto será Nullstellensatz, que nos permitirá convertir una propiedad de nilpotencia en identidades polinomiales.
sala 2
2017-09-13
14:30 hrs.
Seminario Agco
Antoine Hochart. U Chile
Ergodicity of zero-sum stochastic games
República 779 B, Sala 3er Piso.http://www.dii.uchile.cl/acgo/seminar-acgo/
2017-09-13
13:00 hrs.
Seminario de Ingeniería Matemática y Computacional
José Verschae. Escuela de Ingeniería Uc, Facultad de Matemáticas Uc.
El Santo Grial de los algoritmos de aproximación, la maldición de las simetrías, y el nuevo elegido
Auditorio San Agustín. Campus San Joaquín UChttps://goo.gl/4VzQBR
2017-09-12
17:00hrs.
Seminario de Pregrado en Matemáticas
Fernando Figueroa . PUC
Arreglos de rectas reales
Abstract:
Veremos la definición de un erreglo de rectas general, en $$\mathbb{R}$$ y su dual. Para esto último introduciremos el plano proyectivo real, de modo de facilitar los cálculos.
Sala 3
2017-09-12
10:00hrs.
Seminario General - Grupos de Trabajo
Renato Velozo. Facultad de Matemáticas
El teorema de la masa positiva y relatividad general
Abstract:
Este seminario tiene como objetivo exponer el  trabajo clásico de Schoen y Yau "On the proof of the positive mass conjecture in general relativity". A lo largo del semestre se mostrarán diversos trabajos que se relacionan con el objetivo final y que permitirán explicar de mejor manera el teorema de la masa positiva y sus implicancias.
 
El seminario esta orientado a alumnos de avanzados de licenciatura, de magister y de doctorado.
 

sala 3 Facultad de Matemáticas
2017-09-11
16:00hrs.
Seminario Capde
Fethi Mahmoudi. Universidad de Chile
Concentration on curves for a Neumann Ambrosetti-Prodi type problem in two dimensional domains
CMM, U. de Chile, 6to piso, sala multimedia
2017-09-11
15:30hrs.
Seminario de Sistemas Dinámicos
Eduardo Garibaldi. Universidade Estadual de Campinas
An alphabetical approach to the Nivat?s conjecture
Abstract:
Nivat’s conjecture claims that only periodic configurations on a two-dimensional integer lattice may satisfy a low complexity assumption. Since techniques used to address the Nivat’s conjecture usually relies on Morse-Hedlund Theorem, an improved version of this classical result may mean a new step towards a proof for the conjecture. In this talk, we discuss how, following methods highlighted by Cyr and Kra, an extension of the so far best known result to the Nivat’s conjecture may be derived from an alphabetical version of Morse-Hedlund Theorem. This a joint work with C. Colle.
Sala 1, PUC
2017-09-11
5:00pmhrs.
Seminario Capde
Mateo Rizzi. Universidad de Chile
Cahn-Hilliard equation and Willmore surfaces
Abstract:
There are many results in the literature concerning the relation between the Allen-Cahn equation and minimal surfaces. In this talk I will present some analogue results for the Cahn-Hilliard equation, that is a fourth order PDE which is related to the Willmore energy through some Gamma-convergence results. I will present results in dimension 2 and 3, concerning the construction of solutions, and I will briefly discuss some qualitative properties.

CMM, U. de Chile, 6to piso, sala multimediahttp://capde.cl/scientific-activities-2/
2017-09-08
14:30hrs.
Seminario de Geometría Algebraica
Natalia García. PUC Chile
Aplicaciones aritméticas y geométricas de encontrar todas las curvas de género bajo en superficies
Abstract:
Ahora que tenemos más conceptos de la geometría algebraica, vamos a ver en más detalle como se conecta el encontrar curvas de género bajo con resultados aritméticos. Veremos como el encontrar todas las curvas de género bajo de una superficie definida por un sistema de ecuaciones Diofantinas, nos permite:

- Describir todas salvo finitas soluciones del sistema sobre cuerpos de números, bajo la conjetura de Bombieri-Lang. Esto es en el caso que la superficie sea de tipo general;
- Dar todas las soluciones del sistema sobre cuerpos de funciones (por ejemplo polinomios, funciones racionales). Esto es incondicional y no necesita tipo general.

También veremos aplicaciones geométricas, como:

- Encontrar nuevos ejemplos de superficies con finitas curvas de género cero o uno, que no satisfacen los criterios propuestos por Bogomolov para que esto ocurra.
- Encontrar nuevos ejemplos de superficies Brody-hiperbólicas.

El próximo viernes creo que ya estaremos en condiciones para explicar la noción fundamental que se necesita para encontrar todas las curvas de género bajo en una superficie, y empezar a explicar a grandes rasgos el método.

Sala 2
2017-09-08
12:00hrs.
Seminario de Estadística
Daniela Castro. King Abdullah University Of Science And Technology (Saudi Arabia)
Spatial analysis of U.S. precipitation extremes: a local likelihood approach for estimating complex tail dependence structures in high dimensions
Abstract:
In order to model the complex non-stationary dependence structure of precipitation extremes over the entire contiguous U.S., we propose a flexible local approach based on factor copula models. Specifically, by using Gaussian location mixture processes, we assume that there is a common, unobserved, random factor affecting the joint dependence of all measurements in small regional neighborhoods. Choosing this common factor to be exponentially distributed, one can show that the joint upper tail of the resulting copula is asymptotically equivalent to the (max-stable) Hüsler-Reiss copula or its Pareto process counterpart; therefore, the so-called exponential factor copula model captures tail dependence, but unlike the latter, has weakening dependence strength as events become more extreme, a feature commonly observed with precipitation data. In order to describe the stochastic behavior of extreme precipitation events over the U.S., we embed the exponential factor model in a more general non-stationary model, but we fit its local stationary counterpart to high threshold exceedances under the assumption of local stationarity. This allows us to gain in flexibility, while making inference for such a large and complex dataset feasible. Adopting a local censored likelihood approach, inference is made on a fine spatial grid, and local model fitting is performed
taking advantage of distributed computing resources and of the embarrassingly parallel nature of this estimation method. The local model is efficiently fitted at all grid points, and uncertainty is measured using a block bootstrap procedure. Simulation results show that our approach is able to adequately capture complex dependencies on a local scale, therefore providing valuable input for regional risk assessment. Additionally, our data application shows that the model is able to flexibly represent extreme rainfall characteristics on a continental scale. A comparison between past and current U.S. rainfall data suggests that extremal dependence might be stronger nowadays than during the first half of the twentieth century in some areas, which has important implications on regional flood risk assessment.
Sala 2, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chile
2017-09-08
10:00hrs.
Estadística Educacional
Jorge González. Pontificia Universidad Católica de Chile
Nonparametric bounds analysis for NEAT equating
Abstract:
In the nonequivalent groups with anchor tests design (NEAT), two groups of test takers are sampled from two different populations and are assigned only one of two test forms. Additionally, a common anchor test is  dministered to both samples. While probability distributions of anchor scores can be estimated directly from the observed data, the sampling process does not provide information on the score probability distributions or test forms that were not administered. In other words, they are not identified by the data. The equating literature has introduced the concept of synthetic population and strong assumptions that allow to estimate the  non-identified score distributions. In this paper, we offer an alternative to this traditional practice in NEAT equating which uses the partially identified probability distributions to build the equating transformation, thus  voiding the use of any assumption. It is shown that the target score probability distributions and its corresponding quantiles used for equating, are bounded in the partially identified region. The approach is illustrated sing a well known and studied data set in the equating literature. A comparison with the usual approach based on synthetic populations and the equality of conditional score distributions on populations is also presented..
Sala 5 - Facultad de Matemáticas UClies.mat.uc.cl
2017-09-07
15.30hrs.
Seminario de Postgrado en Estadística
Mauricio Castro. Departamento de Estadística, Pontificia Universidad Católica de Chile
Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads
Abstract:

In some acquired immunodeficiency syndrome (AIDS) clinical trials, the human immunodeficiency virus-1 ribonucleic acid measurements are collected irreg- ularly over time and are often subject to some upper and lower detection limits, depending on the quantification assays. Linear and nonlinear mixed-effects models, with modifications to accommodate censored observations, are routinely used to analyze this type of data (Vaida and Liu, J Comput Graph Stat 18:797–817, 2009; Matos et al., Comput Stat Data Anal 57(1):450–464, 2013a). This paper presents a framework for fitting LMEC/NLMEC with response variables recorded at irregular intervals. To address the serial correlation among the within-subject errors, a damped exponential correlation structure is considered in the random error and an EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the likelihood value. The proposed methods are illustrated with simulations and the analysis of two real AIDS case studies.

Joint work with Larissa A. Matos (UNICAMP) and Victor H. Lachos (UCONN).


Sala 3, Facultad de Matemática UC
2017-09-06
13:00 hrs.
Seminario de Ingeniería Matemática y Computacional
Domagoj Vrgoc. Departamento de Ciencia de la Computación, UC
Using theory in practice: Examples and lessons learned
Auditorio San Agustín, UChttps://goo.gl/yAFUmQ
2017-09-06
14:30 hrs.
Seminario Agco
José Fuentes. Dcc, U Chile.
Fast and Compact Planar Embeddings
República 779 B, Sala 3er Piso.http://www.dii.uchile.cl/acgo/seminar-acgo/
2017-09-05
16:00hrs.
Seminario de Análisis y Geometría
Leonelo Iturriaga. Universidad Técnica Federico Santa María
Teoremas de Liouville para soluciones radiales de ecuaciones elípticas semilinales
Abstract:
En esta charla presentaremos algunos teoremas de Liouville para soluciones positivas radialmente simétricas de la ecuación
$$-\Delta u=f(u) \ \text{    en } \mathbb{R}^n$$
donde $f$ es una función continua en $[0,+\infty)$ que es positiva en $(0,+\infty)$. Nuestro enfoque nos permite considerar problemas mas generales, donde la no linealidad puede ser multiplicada por un peso radialmente simétrico y/o el Laplaciano es reemplazado por el $p$-Laplaciano, $1 < p < N$.

Sala 2, Facultad de Matemática
2017-09-04
17:00hrs.
Seminario Capde
Mauricio Romo. Ias, Princeton
Derived Categories, gauge theories and analytic continuation
Abstract:
In this talk I will introduce the concept of Gauged Linear Sigma Model (GLSM), a class of quantum field theories, in mathematical terms. I will show how the GLSM can be used to conjecture derived equivalences (of categories such as coherent sheaves on projective spaces and a matrix factorizations) and how this translates into analytic properties of physical quantities.
Sala 2http://capde.cl/scientific-activities-2/
2017-09-04
16:00hrs.
Seminario Capde
Rémy Rodiac. Université Catholique de Louvain, Bélgica
Axially symmetric minimizers of the neo-Hookean energy in 3D
Abstract:
The neo-Hookean energy is an energy broadly used by physicists and engineers to describe the behavior of elastic materials undergoing large deformations. However to prove the existence of minimizers of this energy is still an open problem. We consider this problem in an axisymmetric setting and show that if the domain do not contain the axis of symmetry then minimizers do exist. Ours axisymmetric minimizers are also solutions of the weak form of the Euler-Lagrange equations of elasticity. This is a joint work with Duvan Henao.

Sala 2http://capde.cl/scientific-activities-2/
2017-09-04
16:00hrs.
Seminario de Probabilidad
Amitai Linker. U. Chile
The Contact Process on Evolving Scale-Free Networks
Abstract:
In this talk we present some results on the contact process running on large scale-free networks, where nodes update their connections at independent random times. We will show that depending on the parameters of the model we can observe either slow extinction for all infection rates, or fast extinction if the infection rate is small enough. This differs from previous results in the case of static scale-free networks where only the first behaviour is observed. We will also show that the analysis of the asymptotic form of the metastable density of the process and its dependency on the model parameters can be used to understand the optimal mechanisms used by the infection to survive. Joint work with Peter Mörters and Emmanuel Jacob.
Sala John Von Neumann, 7mo piso, CMMhttp://nm.cmm.uchile.cl/seminarios/
2017-09-01
10:00hrs.
Estadística Educacional
Jorge González. Pontificia Universidad Católica de Chile
Equating: Una breve introducción
Sala 5 Facultad de Matemáticas UClies.mat.uc.cl
2017-09-01
17:15hrs.
Seminario de Pregrado en Matemáticas
Ricardo Vargas. PUC
Equidisección y el teorema de Monsky
Abstract:
¿Es posible diseccionar un cuadrado en una cantidad impar de triángulos, todos de igual área? Durante este seminario estudiaremos el teorema de Monsky, que nos permite responder esta pregunta cuya formulación es sencilla y aparentemente inocente pero cuya respuesta ocupa inesperadamente resultados e ideas que involucran topología combinatorial (lema de Sperner) y extensiones de valuaciones 2-ádicas (auspiciado por el teorema de Chevalley). Para concluir, comentaremos brevemente algunos resultados y problemas abiertos relacionados.
Sala 2
2017-09-01
14:30hrs.
Seminario de Geometría Algebraica
Giancarlo Urzúa. PUC Chile
Construcción de Cubrimientos de Variedades
sala 2
2017-08-31
17:00hrs.
Seminario de Postgrado en Matemáticas
Nicolás Alvarado. PUC
El problema del Pijama
Abstract:
El conjunto del pijama es la unión de todas las vecindades verticales de radio arbitrariamente pequeño, centradas en los enteros del eje real en el plano complejo. En esta charla mostraremos que es posible cubrir todo el plano complejo usando una cantidad finita de rotaciones de las franjas que componen este conjunto.
Sala 3, Facultad de Matemáticas
2017-08-30
13:00 hrs.hrs.
Seminario de Ingeniería Matemática y Computacional
Alejandro Jara. Departamento de Estadística, Facultad de Matemáticas, UC
Bayesian Nonparametrics and Big Data: Discovering Complex Data Structures
Auditorio San Agustín UChttp://www.ing.uc.cl/ingenieria-matematica/seminario-de-bayesian-nonparametrics-big-data-en-imc/
2017-08-30
14:30 hrs.hrs.
Seminario Agco
Miquel Oliu Barton. Université Paris-Dauphine.
The unknown stochastic game
República 779 B, Sala 3er Piso.http://www.dii.uchile.cl/acgo/seminar-acgo/
2017-08-28
16:30hrs.
Seminario de Sistemas Dinámicos
Rodolfo Gutierrez. Paris Vii
Clasificación de los grupos de Rauzy?Veech
Abstract:
El algoritmo de renormalización de Rauzy–Veech es un poderoso método para el estudio de la dinámica de las transformaciones de intercambios de intervalo y de los flujos de traslación. En efecto, se puede interpretar como una discretización del cociclo Kontsevich–Zorich, que es la parte no trivial de la derivada del flujo de Teichmüller. La acción en homología de este algoritmo es un subgrupo de Sp(2g, Z) y se conoce como un grupo de Rauzy–Veech. En 1999, Zorich conjeturó que estos grupos son densos en Sp(2g, R) para la topología de Zariski. Las consecuencias dinámicas de esta conjetura son múltiples: en particular, generaliza la demostración de Avila–Viana de la conjetura de Kontsevich–Zorich, la que postula la simplicidad del espectro de Lyapunov de casi toda transformación de intercambio de intervalos o flujo de traslación.
 
El trabajo pionero de Avila–Matheus–Yoccoz estableció esta conjetura para el caso hiperelíptico. Expandiendo sus técnicas, es posible encontrar una clasificación completa de los grupos de Rauzy–Veech, demostrando, en particular, la conjetura de Zorich. Por ejemplo, para los estratos conexos de superficies de género g ≥ 3 estos grupos resultan ser Sp(2g, Z).

Sala von Neumann, 7mo piso, CMM
2017-08-28
16:00hrs.
Seminario de Geometría Algebraica
Mikhail Borovoi. Tel Aviv University
Cayley groups
Abstract:
I will start the talk with the definition of the special orthogonal group SO(n) and with the classical "Cayley transform" for SO(n) constructed by Arthur Cayley in 1846. A connected linear algebraic group G over C is called a *Cayley group* if it admits a *Cayley map*, that is, a G-equivariant birational isomorphism between the group variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley group.  A linear algebraic group G is called *stably Cayley* if G x (C^*)^r is Cayley for some natural number r. I will consider semisimple algebraic groups, in particular, simple algebraic groups. I will describe classification of Cayley simple groups and of stably Cayley semisimple groups. (Based on joint works with Boris Kunyavskii and others.)
sala 1, Facultad de Matemáticas
2017-08-25
16:00hrs.
Seminario de Geometría Algebraica
Nicolás Arancibia Robert. Carleton University
Una introducción al principio de funtorialidad de Langlands y a la conjetura local de Arthur
Abstract:
El objetivo de esta charla es dar una introducción a ciertos aspectos del programa de Langlands. Comenzaremos introduciendo ciertos conceptos necesarios para poder enunciar el principio de funtorialidad para luego dar paso al trabajo de James Arthur sobre la clasificación del espectro automorfo discreto de grupos clásicos. Si el tiempo lo permite, daremos una corta introducción al trabajo de J. Adams, D. Barbasch y D. Vogan sobre la descripción a partir de herramientas geométricas de los llamados paquetes d'Arthur.
Facultad de Matemáticas, sala 2
2017-08-25
17:15hrs.
Seminario de Pregrado en Matemáticas
Sebastián Pavez. PUC
Teorema del punto fijo de Brouwer en dimensión 2
Abstract:
Se demostrará el teorema del punto fijo de Brouwer en dimensión 2 usando métodos combinatoriales y coordenadas baricéntricas.
Sala 2
2017-08-25
14:30hrs.
Seminario de Geometría Algebraica
Giancarlo Urzúa. PUC Chile
Elementos de Superficies Algebraicas
sala 2
2017-08-24
10:00hrs.
Estadística Educacional
Ernesto San Martín. Pontificia Universidad Católica de Chile
Modelamiento Estadístico de Fenómenos Educacionales
Abstract:
Durante los últimos dos semestres, hemos desarrollado un seminario educacional focalizado en la teoría psicométrica de espacios de aprendizaje. Este semestre queremos continuar con este seminario, pero ampliándolo a otros problemas de medición y evaluación educacional. En este primer seminario, queremos mostrar un panorama general de problemas educacionales que requieren modelamiento estructural. Este panorama generañ está al menos compuesto por los siguientes temas:

1. Caracterización y existencia de variables latentes en modelos psicométricos.
2. Evaluación de políticas públicas educacionales.
3. Modelamiento de aprendizaje.
4. Equidad e invarianza poblacional.
5. Interacciones sociales.
6. Efectividad de sistemas educacionales.
7. Elección de escuelas.

En esta charla se presentarán problemáticas concretas asociadas a estos temas. además de mostrar en qué medida los mismos están relacionados entre sí. Especial énfasis se dará a los problemas de identificación, mostrando que su solución requiere tanto herramientas matemáticas como consideraciones contextuales y sustantivas.
Sala 3 - Facultad de Matemáticas PUC
2017-08-23
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Carlos Pérez Arancibia. Mit
Integral equation methods for problems of scattering by metasurfaces
Auditorio San Agustínhttp://www.ing.uc.cl/ingenieria-matematica/nuevo-profesor-imc-presenta-seminario-integral-equation-methods-problems-scattering-metasurfaces/
2017-08-21
16:30hrs.
Seminario de Sistemas Dinámicos
Angel Pardo. Université Aix-Marseille
Billares en polígonos, superficies planas y dinámica en espacios de moduli
Sala von Neumann, 7mo piso, CMM
2017-08-21
16:30hrs.
Seminario de Probabilidad
Santiago Saglietti. Technion
On (a proof for) Kesten's theorem on supercritical Branching Brownian Motion with Absorption.
Abstract:
Consider a (continuous time) branching Markov process in which:
  • One starts with a single particle initially located at some x>0, whose position evolves according to a Brownian motion with negative drift  -c which is absorbed upon reaching the origin.
  • This particle waits for an independent random exponential time of parameter r>0 and then branches, dying on the spot and giving birth to a random number m\geq0 of new particles at its current position.
  • These m new particles now evolve independently, each following the same stochastic behavior of their parent (evolve and then branch, and so on…).

It is well-known that if r(E(m)-1)>c^2/2 then this process is supercritical: with positive probability the process does not die out, in the sense that there are particles strictly above the origin for all times.

In this talk we will show that, whenever the process does not die out, as t\to\infty one has that the number of particles at time t inside any given set B grows like its expectation and, furthermore, that its proportion over their total number behaves like the (minimal) quasi-stationary distribution associated to the Brownian motion with drift -c and absorption at 0. In particular, this proves a result stated by Kesten in [1] for which there was no proof available until now.

Joint work with Oren Louidor.

[1] Kesten, H. (1978). Branching Brownian motion with absorption. Stochastic Processes and their Applications7(1), 9-47.


sala 2, Facultad de matemáticas, PUChttp://nm.cmm.uchile.cl/seminarios/
2017-08-18
14:30hrs.
Seminario de Geometría Algebraica
Sergio Troncoso. PUC Chile
Introducción a las nociones básicas en geometría de superficies
Sala 2
2017-08-18
16:00hrs.
Coloquio de Matemática UC
Francois Charette. University Of Ottawa
An overview of Morse theory
Abstract:
Morse theory is an essential tool in the study of manifolds,  objects that look from up close like euclidian space.  For example, think of the surface of the Earth; it looks like a plane, although as a global object, it is certainly not a plane.  In this talk, we will see what Morse theory is and how it can help us understand surfaces better.  Time permitting, I will introduce an infinite dimensional version called Hamiltonian Floer homology, which has been a very useful tool in symplectic topology, my field of research.
Sala 2
2017-08-18
17:15|hrs.
Seminario de Pregrado en Matemáticas
Roberto Maturana. PUC
Marchas aleatorias un buen lugar para comenzar.
Abstract:
Desarrollaremos un modelo sencillo y concreto de marcha aleatoria, a partir de esta comenzaremos a definir conceptos y probar teoremas de la teoría.
Sala 2
2017-08-17
14.00hrs.
Seminario de Postgrado en Estadística
Miguel Uicab . Estudiante, Doctorado Estadística UC
Aplicación de estadística circular en el estudio de la incidencia de dengue en Yucatán, México.
Abstract:

La estadística circular tiene como objeto el estudio de datos a los cuales, a cada uno de ellos, se le asocia una dirección (ángulo), y ésta, a su vez, se identifica con un punto en la circunferencia unitaria, de ahí que reciben el nombre de datos circulares. Estos datos incluyen direcciones medidas usando la brújula y el transportador, así como observaciones provenientes del reloj y de fenómenos periódicos a través del tiempo. Los métodos estadísticos clásicos son inadecuados para analizar este tipo de datos, ya que no toman en cuenta su naturaleza periódica, por lo que se han diseñado estadísticos descriptivos, distribuciones de probabilidad, pruebas de hipótesis y demás herramientas estadísticas específicas para datos circulares.

 

El dengue en el estado mexicano de Yucatán ha permanecido hasta la presente fecha en forma endémica. La incidencia de dengue en aquel estado es un fenómeno periódico, pues su ocurrencia depende, en gran medida, de la temporada de lluvias presente cada año en el estado.

 

El presente trabajo pretende mostrar la aplicación de la herramienta que ofrece la estadística circular, en el estudio del dengue en Yucatán, al dar una descripción de la incidencia de la enfermedad y hacer inferencia estadística acerca de ella. Para tal fin, se han considerado períodos anuales de estudio que se establecen entre los años 2009 y 2017. Un período de estudio consiste en analizar los casos de dengue, registrados semanalmente, que suceden entre el mes de mayo de un año y el mes de abril del año siguiente. Para cada período de estudio, se han realizado un análisis descriptivo y el ajuste de un modelo circular de probabilidad. En cuanto al análisis descriptivo, se hecho uso de la representación gráfica de datos circulares, dada por los diagramas circular y de rosa, y se han calculado estadísticos descriptivos circulares. Para la modelación, se han considerado modelos clásicos y recientes reportados en la literatura de estadística circular, entre las que se encuentran la distribución von Mises (o Normal Circular), la familia de    distribuciones simétricas Jones-Pewsey y la familia de distribuciones flexibles Inversas Batschelet.

 

Como resultado, se han observado estructuras de comportamiento entre los períodos de estudio analizados, que podrían usarse para llevar a cabo acciones de lucha antivectorial más eficientes.

 

(Algunas) Referencias

Jones, M. y Pewsey, A. (2005). A family of symmetric distributions on the circle. Journal of the American Statistical Association, 100(472),1422-1428.

Jones, M. y Pewsey, A. (2012). Inverse Batschelet Distributions for Circular Data. Biometrics, 68(1), 183-193.

Mardia, K. V. y Jupp, P. E. (1999). Directional statistics. John Wiley & Sons. Pewsey, A. (2002). Testing circular symmetry. The Canadian Journal of Statistics, 30(4), 591-600.

Pewsey, A., Neuhauser, M., y Ruxton, G. D. (2013). Circular statistics in R. Oxford University Press.


Sala 3, Facultad de Matemática UC
2017-08-17
17:00hrs.
Seminario de Postgrado en Matemáticas
Jose Torres. PUC
Flujos en Geometría
Abstract:
La charla tratará sobre los flujos en geometría dando una breve descripción en su aporte a la matemática. Además se le dará un especial énfasis al flujo de Ricci y su relación con la conjetura de geometrización de Thurston.
Sala 3, Facultad de Matemáticas
2017-08-14
16:00 hrshrs.
Seminario de Probabilidad
Avelio Sepúlveda. Eth Zurich
A glimpse on excursion theory for the two-dimensional continuum Gaussian free field.
Abstract:
Based on joint work with Juhan Aru, Titus Lupu and Wendelin Werner. Two-dimensional continuum Gaussian free field (GFF) has been one of the main objects of conformal invariant probability theory in the last ten years. The GFF is the two-dimensional analogue of Brownian motion when the time set is replaced by a 2-dimensional domain. Although one can not make sense of the GFF as a proper function, it can be seen as a “generalized function” (i.e. a Schwartz distribution). The main objective of this talk is to go through recent development in the understanding of the analogue, in the GFF context, of Ito’s excursion theory for Brownian motion. As a corollary, we will see how this theory can be used to define the Lévy transform of the GFF.
Sala de seminarios John Von Neumann, 7mo piso, CMMhttp://nm.cmm.uchile.cl/seminarios/
2017-08-11
17:15hrs.
Seminario de Pregrado en Matemáticas
Gabriel Ramírez Raposo. PUC
Paradojas, grupos y geometría. 2.0
Abstract:
En esta charla expondremos algunas aparentes "paradojas" que ocurren en la matemática. Nos enfocaremos principalmente en las paradojas que contradicen la noción de "tamaño" como lo entendemos usualmente. Para ello expondremos algunas paradojas básicas para luego hablar de grupos paradójicos, equidescomponibilidad y entregar las ideas centrales de la demostración de la paradoja de Banach-Tarski. Finalmente y si alcanza el tiempo discutiremos el rol del axioma de elección y cual es el origen de estas paradojas y sus limitaciones frente a la noción de medida.
Sala 2
2017-08-10
17:00hrs.
Seminario de Postgrado en Matemáticas
Rodrigo Bazaes. PUC
Detectando el rastro de una marcha aleatoria en un escenario aleatorio
Abstract:
En esta charla hablaré sobre las ideas principales del artículo $[1]$. Para entender el problema, supongamos que en cada punto de $\mathbb{Z}^{2}$ colocamos una medida $\mu$ de una variable aleatoria Bernoulli de parámetro $1/2$ .Consideremos una marcha aleatoria simple en $\mathbb{Z}^2$, y en cada punto donde pase esta, cambiamos la medida inicial $\mu$ por otra medida $\nu$ de una variable aleatoria Bernoulli de parámetro $p\neq 1/2$. La pregunta es, ¿Podemos distinguir las medidas $\mu$ y $\nu$?. Presentaremos este problema en un poco más de generalidad, y veremos que en el caso de la marcha simple, la respuesta no depende de la dimensión.

Referencias:
$[1]$ Noam Berger, Yuval Peres, et al. Detecting the trail of a random walker in a random scenery. Electronic Journal of Probability, 18, 2013.
Sala 3, Facultad de Matemáticas
2017-08-10
17:00hrs.
Seminario de Teoría Espectral
Soeren Fournais. Aarhus Universiy
A Hardy-Lieb-Thirring inequality for fractional Pauli operators
Abstract:
In this talk we will discuss recent work on Hardy-Lieb-Thirring inequalities for the Pauli operator. The classical Lieb-Thirring inequality estimates the sum of the negative eigenvalues of a Schrödinger operator
$-\Delta + V$ by an integral of a power of the potential. In $3$-dimensions, this becomes
$$
\operatorname{tr}( - \Delta + V)_{-} \leq C \int (V(x))_{-}^{5/2}\,dx
$$
The classical Hardy inequality states that (also in $3D$),
$$
-\Delta - \frac{1}{4 |x|^2} \geq 0,
$$
where the constant $\frac{1}{4}$ is the sharp constant for this bound.

It is well known, that these inequalities can be combined to yield "Hardy-Lieb-Thirring inequalities”, i.e. the Lieb-Thirring inequality above still holds (possibly with a different constant) if $V$ is replaced by $- \frac{1}{4 |x|^2} + V$ on the left side.

In this talk we will discuss similar inequalities, where the non-relativistic kinetic energy operator $-\Delta$ is replaced by a magnetic Pauli operator. In particular, we will discuss a relativistic version, where the kinetic energy is the square root of a Pauli operator, and where $ \frac{1}{4 |x|^2}$ is replaced by $\frac{c_H}{|x|}$, with $c_H$ being the critical Hardy constant for the relativistic problem.

This is joint work with Gonzalo Bley.
Sala 1
2017-08-04
14:30hrs.
Seminario de Geometría Algebraica
Natalia García Fritz. PUC Chile
Puntos racionales y problemas Diofantinos
sala 2
2017-08-04
15:30hrs.
Seminario de Pregrado en Matemáticas
Néstor Jofré. PUC
Análisis numérico del método del punto fijo en R sobre la solución de la ecuación de Colebrook-White 2.0
Abstract:
La necesidad de metodos numéricos para hallar una aproximación a soluciones que no pueden ser obtenidas de forma analítica es cada vez mayor. La ecuación de Colebrook-White representa un esfuerzo de modelamiento que relaciona determinadas ciertas asociadas al flujo de un fluído que transita por zonas tubulares con un coeficiente de roce $$\lambda$$, el cual será el parámetro a resolver. 

Se buscará garantizar la existencia y unicidad teórica (local y global) de la solución mediante herramientas de analisis matemático en un entorno factible consistente, dentro de las cuales se encuentra el teorema del punto fijo de Brouwer en $$\mathbb{R}$$. Ademas, bajo determinadas condiciones, se hará uso el método iterativo del punto fijo para hallar una aproximacion a la solución, desde distintos puntos iniciales para mostrar la efectividad y convergencia del mismo respecto de dicha solución.
Por confirmar (Facultad de Matemática)
2017-08-03
10:00hrs.
Estadística Educacional
Jorge González. Pontificia Universidad Católica de Chile
Segunda Charla Estadística Educacional
Abstract:
Resumen por publicar.
Sala 3lies.mat.uc.cl
2017-07-28
15:30hrs.
Seminario de Pregrado en Matemáticas
Eduardo Oregón . PUC
El plano hiperbólico
Abstract:
Presentaremos este modelo geométrico que no respeta el quinto postulado de Euclides. Discutiremos algunas de sus semejanzas y diferencias respecto al plano Euclídeo, principalmente en términos de su conjunto de isometrías. Si el tiempo lo permite, se verán ejemplos del rol que cumple esta construcción en la matemática moderna.
Sala 1
2017-07-21
15:40-17:00hrs.
Seminario de Geometría Algebraica
Paolo Stellari. Universidad de Milan
Cubic threefolds and fourfolds: geometry and homological algebra III
Abstract:
We revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.
Sala 1https://raizdepie.wixsite.com/algebraic-geometry
2017-07-21
14:00hrs.
Seminarios Extraordinarios
Paolo Stellari, Marcello Bernardara. Pontificia Universidad Católica de Chile
Derived Techniques In Classical Algebraic Geometry
Abstract:
La Facultad de Matemáticas de la Pontificia Universidad Católica invita a profesores y estudiantes a participar de una serie de mini-cursos que se realizarán entre los días 19 y 21 de julio del año 2017.
 
 
En esta serie de mini-cursos se discutirá el uso de técnicas derivadas en la geometría algebraica clásica. El primer curso estará a cargo del profesor del departamento de Matemáticas de la Universidad de Milan, Paolo Stellari, quien hablará sobre la geometría de los cúbicos. El segundo curso lo dictará el profesor de la Universidad de Toulose, Marcello Bernardara. Sus mini-cursos estaran relacionados a los nuevos métodos derivados en el estudio de cuestiones de racionalidad.

Sala 1 Facultad de Matemáticas
2017-07-21
14:00-15:20hrs.
Seminario de Geometría Algebraica
Marcello Bernardara. Universidad de Toulose
Derived categories, cycles, and rationality
Abstract:
In the last decades, semiorthogonal decompositions of derived categories of coherent sheaves have been considered as a possible tool to attack birationality questions. Since the seminal work of Bondal and Orlov, the work of many authors, Kuznetsov above all of them, has made clear what we should expect and which are the main technical problems. In particular, one would expect that the derived category of a rational variety must be decomposed in "codimension 2" subcategories.

The aim of these lectures is to set definitions and property that could give a sense to the above considerations, and to show that this conjectural obstruction is stronger than the known classical ones in cases such as surfaces or Fano threefolds, and closely related for some particular fourfold (cubic, Gushel'-Mukai). A particular attention will be put on constructions related to cycles and motives, such as intermediate Jacobians and decomposition of the diagonal.
Sala 1https://raizdepie.wixsite.com/algebraic-geometry
2017-07-21
17:00hrs.
Seminario de Pregrado en Matemáticas
Gabriel Ramírez Raposo. PUC
Paradojas y geometría.
Abstract:
En esta charla expondremos algunas aparentes "paradojas" que ocurren en la matemática. Nos enfocaremos principalmente en las paradojas que contradicen la noción de "tamaño" como lo entendemos usualmente. Para ello expondremos algunas paradojas básicas para luego hablar de grupos paradójicos, equidescomponibilidad y entregar las ideas centrales de la demostración de la paradoja de Banach-Tarski. Finalmente y si alcanza el tiempo discutiremos el rol del axioma de elección y cual es el origen de estas paradojas y sus limitaciones frente a la noción de medida.
Sala 2
2017-07-20
14:00hrs.
Seminarios Extraordinarios
Paolo Stellari, Marcello Bernardara. Pontificia Universidad Católica de Chile
Derived Techniques In Classical Algebraic Geometry
Abstract:
La Facultad de Matemáticas de la Pontificia Universidad Católica invita a profesores y estudiantes a participar de una serie de mini-cursos que se realizarán entre los días 19 y 21 de julio del año 2017.
 
 
En esta serie de mini-cursos se discutirá el uso de técnicas derivadas en la geometría algebraica clásica. El primer curso estará a cargo del profesor del departamento de Matemáticas de la Universidad de Milan, Paolo Stellari, quien hablará sobre la geometría de los cúbicos. El segundo curso lo dictará el profesor de la Universidad de Toulose, Marcello Bernardara. Sus mini-cursos estaran relacionados a los nuevos métodos derivados en el estudio de cuestiones de racionalidad.

Sala 1 Facultad de Matemáticas https://raizdepie.wixsite.com/algebraic-geometry
2017-07-20
15:40-17:00hrs.
Seminario de Geometría Algebraica
Paolo Stellari. Universidad de Milan
Cubic threefolds and fourfolds: geometry and homological algebra II
Abstract:
We revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.
Sala 1https://raizdepie.wixsite.com/algebraic-geometry
2017-07-20
14:00-15:20hrs.
Seminario de Geometría Algebraica
Marcello Bernardara. Universidad de Toulose
Derived categories, cycles, and rationality II
Abstract:
In the last decades, semiorthogonal decompositions of derived categories of coherent sheaves have been considered as a possible tool to attack birationality questions. Since the seminal work of Bondal and Orlov, the work of many authors, Kuznetsov above all of them, has made clear what we should expect and which are the main technical problems. In particular, one would expect that the derived category of a rational variety must be decomposed in "codimension 2" subcategories.

The aim of these lectures is to set definitions and property that could give a sense to the above considerations, and to show that this conjectural obstruction is stronger than the known classical ones in cases such as surfaces or Fano threefolds, and closely related for some particular fourfold (cubic, Gushel'-Mukai). A particular attention will be put on constructions related to cycles and motives, such as intermediate Jacobians and decomposition of the diagonal.
Sala 1https://raizdepie.wixsite.com/algebraic-geometry
2017-07-19
14:00hrs.
Seminarios Extraordinarios
Paolo Stellari, Marcello Bernardara. Pontificia Universidad Católica de Chile
Derived techniques in classical algebraic geometry
Abstract:
La Facultad de Matemáticas de la Pontificia Universidad Católica invita a profesores y estudiantes a participar de una serie de mini-cursos que se realizarán entre los días 19 y 21 de julio del año 2017.


En esta serie de mini-cursos se discutirá el uso de técnicas derivadas en la geometría algebraica clásica. El primer curso estará a cargo del profesor del departamento de Matemáticas de la Universidad de Milan, Paolo Stellari, quien hablará sobre la geometría de los cúbicos. El segundo curso lo dictará el profesor de la Universidad de Toulose, Marcello Bernardara. Sus mini-cursos estaran relacionados a los nuevos métodos derivados en el estudio de cuestiones de racionalidad.

Sala 1 Facultad de Matemáticas https://raizdepie.wixsite.com/algebraic-geometry
2017-07-19
14:00-15:20hrs.
Seminario de Geometría Algebraica
Marcello Bernardara. Universidad de Toulose
Derived categories, cycles, and rationality I
Abstract:
In the last decades, semiorthogonal decompositions of derived categories of coherent sheaves have been considered as a possible tool to attack birationality questions. Since the seminal work of Bondal and Orlov, the work of many authors, Kuznetsov above all of them, has made clear what we should expect and which are the main technical problems. In particular, one would expect that the derived category of a rational variety must be decomposed in "codimension 2" subcategories.

The aim of these lectures is to set definitions and property that could give a sense to the above considerations, and to show that this conjectural obstruction is stronger than the known classical ones in cases such as surfaces or Fano threefolds, and closely related for some particular fourfold (cubic, Gushel'-Mukai). A particular attention will be put on constructions related to cycles and motives, such as intermediate Jacobians and decomposition of the diagonal.
Sala 1https://raizdepie.wixsite.com/algebraic-geometry
2017-07-19
15:40-17:00hrs.
Seminario de Geometría Algebraica
Paolo Stellari. Universidad de Milan
Cubic threefolds and fourfolds: geometry and homological algebra I
Abstract:
We revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.g derived categories and Bridgeland stability conditions. The examples we want toWe revisit some classical results concerning the geometry of smooth cubic hypersurfaces of dimension 3 and 4 by means of modern techniques involving derived categories and Bridgeland stability conditions. The examples we want to examine are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds. are: the Fano variety of lines, twisted cubics curves on cubic fourfolds and the Torelli theorem for cubic threefolds and fourfolds.
Sala 1https://raizdepie.wixsite.com/algebraic-geometry
2017-07-14
17:00hrs.
Seminario de Pregrado en Matemáticas
Néstor Jofré. PUC
Análisis numérico del método del punto fijo en R sobre la solución de la ecuación de Colebrook-White
Abstract:
La necesidad de metodos numéricos para hallar una aproximación a soluciones que no pueden ser obtenidas de forma analítica es cada vez mayor. La ecuación de Colebrook-White representa un esfuerzo de modelamiento que relaciona determinadas ciertas asociadas al flujo de un fluído que transita por zonas tubulares con un coeficiente de roce $$\lambda$$, el cual será el parámetro a resolver.

Se buscará garantizar la existencia y unicidad teórica (local y global) de la solución mediante herramientas de analisis matemático en un entorno factible consistente, dentro de las cuales se encuentra el teorema del punto fijo de Brouwer en $$\mathbb{R}$$. Ademas, bajo determinadas condiciones, se hará uso el método iterativo del punto fijo para hallar una aproximacion a la solución, desde distintos puntos iniciales para mostrar la efectividad y convergencia del mismo respecto de dicha solución.
Sala 2
2017-07-14
14:00-16:00hrs.
Seminario de Geometría Algebraica
Sukhendu Mehrotra. PUC
Introducción a las categorías derivadas en la geometría algebraica I-II
Abstract:
Estas son charlas preparatorias para los mini-cursos de la próxima semana.
Sala 2
2017-07-13
14:00hrs.
Estadística Educacional
Rodrigo Vargas. Pontificia Universidad Católica de Chile
Construcción de un Espacio de Conocimiento - Querying Experts
Abstract:
En esta sesión se mostrará el método de construcción teórica de un Espacio de Conocimiento basado en la consulta a expertos. 
Sala 1
2017-07-11
14:00hrs.
Estadística Educacional
Danny Avello. Pontificia Universidad Católica de Chile
Neo-Classical Test Theory
Abstract:

Las variables latentes en psicometría son ampliamente utilizadas. El efecto escuela en los modelos de Valor Agregado y la habilidad en los modelos de Teoría de Respuesta al Ítem (TRI) son variables latentes. Nuestro estudio busca mejorar nuestro entendimiento sobre las variables latentes en psicometría en el contexto de la Teoría Clásica de Test (TCT).

 

La TCT es el marco referencial más general en psicometría. De Boeck (2004) demostró que utilizando la axiomatización de la TCT de Lord y Novick (1968), los modelos TRI pueden ser incluidos en la TCT como modelos lineales generalizados. Por esto estudiar las variables latentes en la TCT otorga generalidad a nuestros resultados.  

 

Continuando el trabajo realizado por Zimmerman (1975) nosotros utilizamos la dualidad y la geometría de los operadores lineales en Espacios de Hilbert para nuestro estudio. Como producto interno utilizamos la esperanza del producto de dos vectores (variables aleatorias).

 

Algunos de nuestros resultados son: a) Hemos desarrollado una definición multidimensional de confiabilidad; b) Hemos demostrado que bajo la versión débil del axioma de independencia local (ortogonalidad condicional), el kernel del Estimador Empírico de Bayes es vacío, es decir toda la información observable es útil para estimarlo; c) Bajo la versión débil del axioma de independencia local hemos podido identificar la variable latente en la TCT como la proyección ortogonal de lo observado en el spam formado por la variable latente de interés (Valor Verdadero en la jerga de TCT) y d) Bajo la versión débil del axioma de independencia local hemos podido estimar la distribución marginal de la variable latente, y no suponerla normal (0,1) como usualmente se hace.

 

La consecuencia práctica más relevante de estos resultados es la mejora inmediata de la asignación de puntajes/niveles en pruebas estandarizadas. A pesar que lo que motiva la construcción de una prueba es la habilidad cognitiva de interés, representada por una variable latente, en el proceso de asignación de puntajes/niveles se asume su distribución marginal. Es decir que al poder estimar su distribución se mejora la justicia y exactitud de todas las decisiones en política educacional que se toman a partir de los puntajes/niveles asignados a las personas e instituciones.

 

 

 

 

 

 

 

 

 

 

Bibliografía:

 

P. De Boeck and M. Wilson. (2004). Explanatory Item Response Models. A Genera- lized

 

Linear and Nonlinear Approach. Springer, New York, USA.

 

D. Lord and M. Novick .(1968). Statistical Theories of Mental Test Score. Addison Wesley.

 

D. Zimmerman.(1975). Probability Spaces, Hilbert Spaces, and The Axioms of Test Theory. Psychometrika, 40 (3), 395-412.


Sala 1
2017-07-10
16:30hrs.
Seminario de Sistemas Dinámicos
Wenbo Sun. Ohio State University
Equidistribution of dilated curves.
Abstract:

Consider a light source located in a polynomial room. It is a classic question whether the whole room is illuminated by the light. This question was recently settled by Leli?evre, Monteil and Weiss. In this talk, we study the variation on the illumination problem introduced by Chaika and Hubert in the context of closed curves on nilmanifolds. We give necessary and suffcient conditions for a nilmanifold being illuminated by a curve.

 

Sala von Neumann, 7mo piso, CMM
2017-07-07
12:00hrs.
Seminario de Estadística
Gabriel Muñoz. Pontificia Universidad Católica de Chile
Identificación en modelos tipo Rasch, convirtiendo 1PL-AG en 2*1PL
Abstract:

La identificabilidad en los modelos tipo Rasch es de suma importancia ya que establece una biyección entre los parámetros identifi cados por naturaleza y los parámetros de interés. Mientras en algunos de estos modelos ha sido posible identifi car los parámetros de interés (1PL, 1PL-G 2PL), en otros aun es un problema abierto (1PL-AG, 3PL). Las técnicas usualmente usadas para resolver estos problemas relacionan los parámetros de interés entre si, para luego fijar restricciones sobre el espacio paramétrico. En esta charla, se mostrará una forma de relacionar modelos distintos (1PL-AG con 1PL y 3PL con 2PL) para buscar la identi ficación de los parámetros de interés a partir de resultados obtenidos en modelos más sencillos.


Sala 2, Facultad de Matemáticas
2017-07-06
15:30hrs.
Seminario de Pregrado en Matemáticas
Nicolás Vilches. PUC
Vallas, vías de tren y construcción de los reales.
Abstract:
Buscaremos conversar brevemente las construcciones estándar de los números reales y presentar una menos conocida, en la que se ve a los reales como funciones casi lineales. Mostraremos por qué de hecho las operaciones con las que dotamos a este conjunto de funciones surgen de manera natural, y comentaremos a grandes rasgos la demostración de que éstas convierten al conjunto en un cuerpo isomorfo a los reales.
SAM
2017-07-06
17:00hrs.
Seminario de Postgrado en Matemáticas
Felipe Riquelme. Pontificia Universidad Católica de Valparaíso
Entropía de difeomorfismos en variedades Riemannianas
Abstract:
En esta charla discutiremos diferentes resultados relacionados a la entropía de difeomorfismos en variedades Riemannianas, tales como la desigualdad de Ruelle y la formula de Pesin. Abordaremos primero la teoría clásica sobre espacios compactos y discutiremos luego algunos resultados recientes sobre espacios no compactos.
Sala 3, Facultad de Matemáticas
2017-07-04
16:00hrs.
Seminario de Geometría Algebraica
Héctor Pastén. Harvard University
Avances recientes en la conjetura abc
Abstract:
Luego de un breve recuento de los métodos y resultados existentes en relación a la conjetura abc, voy a dar un esbozo una técnica nueva basada en curvas de Shimura y voy a explicar el tipo de resultados incondicionales que permite obtener.
Sala 2, Facultad de Matemáticas
2017-07-04
14:00hrs.
Estadística Educacional
Rodrigo Vargas. Pontificia Universidad Católica de Chile
Espacios de conocimiento y teoria de medios
Abstract:
En esta útima sesió de Teoría de Medios se establecerá la relación entre un medio y un espacio de aprendizaje.
Sala 2, Facultad de Matemáticas.
2017-06-30
09:30hrs.
Seminarios Extraordinarios
Jessika Camaño, Gabriel Gatica, Norbert Heuer, Ricardo Oyarzúa. Facultad de Matemáticas
Santiago Numérico III
Abstract:
The Facultad de Matemáticas of the Pontificia Universidad Católica de Chile (PUC) is proud to host the Ninth Meeting on Numerical Analysis of Partial Differential Equations. The workshop is open to all researchers working or interested in the field, and you are invited to contribute a presentation on your current work. We encourage in particular graduate students to participate; there is some financial support available. As in our previous meetings, the idea of this workshop is for Chilean researchers and colleagues from abroad to meet and to continue or start collaborations and to learn about new activities in the area.
Auditorio Erika Himmel König, del Centro Mide UC
2017-06-30
18:00hrs.
Seminarios Extraordinarios
Apala Majumdar. University Of Bath
Mini-Curso Cristales Líquidos "6. Case Studies of Mathematical Modelling"
Abstract:
An expert in the mathematics and modelling of liquid crystals, Dr. Majumdar has made important contributions to the powerful continuum Landau-de Gennes theory working extensively at the interface of rigorous analysis, challenging simulations and modelling of applications. Her work has been supported by the prestigious fellowships of the Royal Commission for the Exhibition of 1851, the Oxford Centre for Collaborative Applied Mathematics, and the UK EPSRC, and recorgnized with the British Liquid Crystal Society Young Scientist Prize in 2012 and the London Mathematical Society Anne Bennett Prize in 2015.
Sala J. Von Neumann CMM U. de Chile
2017-06-30
12:00 hrshrs.
Seminario de Estadística
Giovanni Motta. Pontificia Universidad Católica de Chile
Cholesky decomposition for time-varying covariances and auto-covariances
Abstract:

In this work we introduce a positive definite non-parametric estimator of the covariance matrix while permitting different smoothing parameters. This estimator is based on the Cholesky decomposition of a pre-estimator of the covariance matrix.

Kernel-type smoothers of the cross-products are based on the same bandwidth for all the variances and co-variances. Though this approach guarantees positive semi-definiteness of the estimated covariance matrix, the use of one common bandwidth for all the entries might be restrictive, as variances and co-variances are in general characterized by different degrees of smoothness. On the other hand, a kernel-type estimator based on different smoothing parameters may deliver an estimated matrix which is not necessarily positive semi-definite. The estimator we propose in this paper is based on the Cholesky decomposition of a preliminary raw estimate of the local covariances. This new approach allows for different smoothing bandwidths while preserving positive definiteness. This approach is particularly appealing for locally stationary time series. In particular, we address the estimation problems for two types of time-varying covariance matrices: the contemporaneous covariance matrix of a multivariate non-stationary time series, and the auto-covariance matrix of a univariate non-stationary time series.


Sala 2, Facultad de Matemáticas
2017-06-30
17:15hrs.
Seminario de Pregrado en Matemáticas
Fernando Figueroa. PUC
Demostraciones no constructivas de existencia
Abstract:
Estamos bastante acostumbrados a que para demostrar la existencia de un elemento con cierta propiedad, simplemente encontremos un ejemplo. Vamos a ver situaciones en que resulta bastante más sencillo demostrar la existencia que encontrar un ejemplo.
SAM
2017-06-30
16:00hrs.
Coloquio de Matemática UC
Ricardo Menares. Pucv
Correspondencias de Hecke e intersecciones improbables
Abstract:
Gran parte de la teoría de números está motivada por entender
el conjunto de soluciones enteras de ecuaciones polinomiales, llamadas
ecuaciones diofantinas. La pregunta básica es saber si el número de
soluciones es finito o infinito. Hasta buena parte del siglo pasado,
cada ecuación era un mundo y el análisis se hacía caso por caso.

Recientemente, ha emergido un principio de "intersecciones
improbables" que explica la finitud o infinitud del conjunto
diofántico estudiado. En la mayoría de los casos en que se aplica este
principio, va de la mano de una propiedad de equidistribución de
puntos algebraicos.

En esta charla explicaremos la filosofía general de las intersecciones
improbables, así como una instancia de este principio obtenida en el
contexto de las curvas elípticas, en colaboración con Sebastián
Herrero y Juan Rivera-Letelier. Más específicamente, mostramos que el
conjunto de curvas elípticas con multiplicación compleja cuyo
invariante j satisface ciertas propiedades diofánticas, es finito.
Deducimos este resultado de una propiedad de equidistribución para
órbitas de correspondencias de Hecke.

No asumiremos que la audiencia está familiarizada con los términos
técnicos que figuran en el párrafo anterior. Si el tiempo lo permite,
indicaremos posibles direcciones de trabajo futuro.
sala 2, Facultad de Matemáticas
2017-06-29
18:00hrs.
Seminarios Extraordinarios
Apala Majumdar. University Of Bath
Mini-Curso Cristales Líquidos "5. The Lyuksyutov low-temperature limit of the Landau-de Gennes theory"
Abstract:
An expert in the mathematics and modelling of liquid crystals, Dr. Majumdar has made important contributions to the powerful continuum Landau-de Gennes theory working extensively at the interface of rigorous analysis, challenging simulations and modelling of applications. Her work has been supported by the prestigious fellowships of the Royal Commission for the Exhibition of 1851, the Oxford Centre for Collaborative Applied Mathematics, and the UK EPSRC, and recorgnized with the British Liquid Crystal Society Young Scientist Prize in 2012 and the London Mathematical Society Anne Bennett Prize in 2015.
Sala J. Von Neumann CMM U. de Chile
2017-06-29
09:30hrs.
Seminarios Extraordinarios
Jessika Camaño, Gabriel Gatica, Norbert Heuer, Ricardo Oyarzúa. Facultad de Matemáticas
Santiago Numérico III
Abstract:
The Facultad de Matemáticas of the Pontificia Universidad Católica de Chile (PUC) is proud to host the Ninth Meeting on Numerical Analysis of Partial Differential Equations. The workshop is open to all researchers working or interested in the field, and you are invited to contribute a presentation on your current work. We encourage in particular graduate students to participate; there is some financial support available. As in our previous meetings, the idea of this workshop is for Chilean researchers and colleagues from abroad to meet and to continue or start collaborations and to learn about new activities in the area.
Auditorio Erika Himmel König, del Centro Mide UChttp://www.ci2ma.udec.cl/SN-III/
2017-06-28
08:30hrs.
Seminarios Extraordinarios
Jessika Camaño, Gabriel Gatica, Norbert Heuer, Ricardo Oyarzúa. Facultad de Matemáticas
Santiago Numérico III
Abstract:
The Facultad de Matemáticas of the Pontificia Universidad Católica de Chile (PUC) is proud to host the Ninth Meeting on Numerical Analysis of Partial Differential Equations. The workshop is open to all researchers working or interested in the field, and you are invited to contribute a presentation on your current work. We encourage in particular graduate students to participate; there is some financial support available. As in our previous meetings, the idea of this workshop is for Chilean researchers and colleagues from abroad to meet and to continue or start collaborations and to learn about new activities in the area.
Auditorio Erika Himmel König, del Centro Mide UChttp://www.ci2ma.udec.cl/SN-III/
2017-06-27
15:30hrs.hrs.
Seminario de Pregrado en Matemáticas
Oscar Chacón. PUC
La curva trisectriz de distancia
Abstract:
En este seminario realizaremos una construcción geométrica con resultados profundos. Dados dos puntos p y q en el plano, los separaremos por dos curvas C1 y C2 tales que cada punto de C1 esté a la misma distancia de p y C2, y cada punto de C2 esté a la misma distancia de C1 y q. Mostraremos, usando geometría elemental, que tales curvas C1 y C2 existen y son únicas. Además, si p=(0,1) y q=(0,-1), entonces C1 es la gráfica de una función f: R -> R, C2es la gráfica de -f, y f es convexa.
Sala 2, Facultad de Matemáticas
2017-06-27
16:00hrs.
Seminario de Probabilidad
Julian Tugaut. Université Jean Monnet
Exit time of a self-stabilizing diffusion
Abstract:
In this talk, we briefly present some Freidlin and Wentzell results then we give a Kramers’type law satisfied by the McKean-Vlasov diffusion when the confining potential is uniformly strictly convex. We briefly present two previous proofs of this result before giving a third proof which is simpler, more intuitive and less technical.
sala John Von Neumann, 7mo piso, CMM, U. Cjile http://nm.cmm.uchile.cl/seminarios/
2017-06-27
18hrs.
Seminarios Extraordinarios
Apala Majumdar. University Of Bath
Mini-Curso Cristales Líquidos "4. The Oseen-Frank limit of the Landau-de Gennes theory"
Abstract:
An expert in the mathematics and modelling of liquid crystals, Dr. Majumdar has made important contributions to the powerful continuum Landau-de Gennes theory working extensively at the interface of rigorous analysis, challenging simulations and modelling of applications. Her work has been supported by the prestigious fellowships of the Royal Commission for the Exhibition of 1851, the Oxford Centre for Collaborative Applied Mathematics, and the UK EPSRC, and recorgnized with the British Liquid Crystal Society Young Scientist Prize in 2012 and the London Mathematical Society Anne Bennett Prize in 2015.
Auditorio Ninoslav Bralic Facultad de Matemáticas PUC
2017-06-27
14:00hrs.
Estadística Educacional
Sandra Garrido. Pontificia Universidad Católica de Chile
Introducción a los Espacios de Conocimiento/Aprendizaje
Abstract:
En esta sesión se hará un resumen introductorio a los Espacios de Conocimiento, Espacios de Aprendizaje y conceptos asociados.
Sala 2 Facultad de Matemáticas
2017-06-23
12:00hrs.
Seminario de Estadística
Carlos Sing-Long. Ingeniería Matemática y Computacional Escuela de Ingeniería
Computational Methods for Unbiased Risk Estimation
Abstract:

In many engineering applications, one seeks to estimate, recover or reconstruct an unknown object of interest from an incomplete set of linear measurements. Mathematically, the unknown object can be represented as the solution to an underdetermined system of linear equations. In recent years it has been shown that it is possible to recover the true object by exploiting a priori information about its structure, such as sparsity in compressed sensing or low-rank in matrix completion. However, in practice the measurements are corrupted by noise and exact recovery is not possible.

A popular approach to address this issue is to solve an unconstrained convex optimization problem to obtain an estimate that both explains the measurements and resembles the known structural characteristics of the true object. The objective function quantifies the trade-off between data fidelity and structural fidelity, which is usually controlled by a single regularization parameter. One possible criterion for selecting the value of this parameter is to minimize an unbiased estimate for the prediction error as a surrogate for the true prediction risk. Unfortunately, evaluating this estimate requires an expression for the weak divergence of the predicted observations. Therefore, it is necessary to characterize the regularity of the solution to the convex optimization problem with respect to the measurements.

In this talk I will present a conceptual and practical framework to study the regularity of the solution to a popular class of such optimization problems. The approach consists of using an auxiliary optimization problem that characterizes the smoothness of the predicted observations. In particular, we can relate the analytic singularities of the predicted observations with the geometric singularities of the feasible set to this problem. I will then present a disciplined approach for obtaining closed-form expressions for the derivatives of the predicted measurements that are amenable to computation. Finally, I will explain how the expressions establish a connection between the geometry of the convex optimization problem and the unbiased estimate for the prediction risk.


Sala 2, Facultad de Matemáticas
2017-06-23
18:00hrs.
Seminarios Extraordinarios
Apala Majumdar. University Of Bath
Mini-Curso Cristales Líquidos "3. The Landau-De Gennes Theory For Nematic Liquid Crystals"
Abstract:
An expert in the mathematics and modelling of liquid crystals, Dr. Majumdar has made important contributions to the powerful continuum Landau-de Gennes theory working extensively at the interface of rigorous analysis, challenging simulations and modelling of applications. Her work has been supported by the prestigious fellowships of the Royal Commission for the Exhibition of 1851, the Oxford Centre for Collaborative Applied Mathematics, and the UK EPSRC, and recorgnized with the British Liquid Crystal Society Young Scientist Prize in 2012 and the London Mathematical Society Anne Bennett Prize in 2015.
Auditorio Ninoslav Bralic Facultad de Matemáticas PUC
2017-06-22
17:00hrs.
Seminario de Postgrado en Matemáticas
Gastón Burrull. PUC
Objetos indescomponibles en las categorías de Hecke.
Abstract:
 En esta charla, introduciremos algunas nociones y motivaciones básicas a los grupos de reflexión finitos (y más generalmente sistemas de Coxeter) y sus correspondientes álgebras de Iwahori-Hecke. Además, presentaremos algunas categorías denominadas "categorías de Hecke" que categorifican las álgebras de Hecke y nos dan más información sobre el objeto básico con un nivel más alto de estructura. Se presentarán los bimódulos Soergel y la categoría diagramática como ejemplos de estas categorías y se presentará el problema fundamental de encontrar explícitamente los objetos indescomponibles en estas categorías. Mostraremos la respuesta en cualquier grupo universal de Coxeter cuando la característica sea cero, este resultado se debe a un trabajo reciente de B. Elias y N. Libedinsky. Si el tiempo lo permite, mostraremos nuestras conjeturas para el caso cuando la característica sea positiva.
Sala 3, Facultad de Matemáticas
2017-06-22
18:00hrs.
Seminarios Extraordinarios
Apala Majumdar. University Of Bath
Mini-Curso Cristales Líquidos "2. The Oseen-Frank theory for nematic liquid crystals, harmonic maps and defects"
Abstract:
An expert in the mathematics and modelling of liquid crystals, Dr. Majumdar has made important contributions to the powerful continuum Landau-de Gennes theory working extensively at the interface of rigorous analysis, challenging simulations and modelling of applications. Her work has been supported by the prestigious fellowships of the Royal Commission for the Exhibition of 1851, the Oxford Centre for Collaborative Applied Mathematics, and the UK EPSRC, and recorgnized with the British Liquid Crystal Society Young Scientist Prize in 2012 and the London Mathematical Society Anne Bennett Prize in 2015.
Auditorio Ninoslav Bralic Facultad de Matemáticas PUC
2017-06-21
16:00hrs.
Seminarios Extraordinarios
Apala Majumdar. University Of Bath
Mini-Curso Cristales Líquidos "1. Introduction to the Mathematics and Physics"
Abstract:
An expert in the mathematics and modelling of liquid crystals, Dr. Majumdar has made important contributions to the powerful continuum Landau-de Gennes theory working extensively at the interface of rigorous analysis, challenging simulations and modelling of applications. Her work has been supported by the prestigious fellowships of the Royal Commission for the Exhibition of 1851, the Oxford Centre for Collaborative Applied Mathematics, and the UK EPSRC, and recorgnized with the British Liquid Crystal Society Young Scientist Prize in 2012 and the London Mathematical Society Anne Bennett Prize in 2015.
Sala J. Von Neumann CMM U. de Chile
2017-06-20
14:00hrs.
Estadística Educacional
Rodrigo Vargas. Pontificia Universidad Católica
Relación entre medios y espacios de aprendizaje - Segunda parte
Abstract:
Esta charla se centra en la relación entre colecciones bien clasificadas (en particular, Espacios de aprendizaje) y los medios, definidos en la sesión anterior.
Sala 2
2017-06-19
16:30hrs.
Seminario de Sistemas Dinámicos
Anibal Velozo. Princeton University
Entropy theory for geodesic flows
Abstract:
The geodesic flow on negatively curved manifolds is one of the classical examples of  Anosov flows. In this talk I will review the main features of the ergodic theory for the geodesic flow on negatively curved manifolds, which are not necessarily compact. We will then focus on the study of the entropy map for such systems. In the non-compact setting a sequence of probability measures can lose mass. A novel feature of our result is that relates the escape of mass of a sequence of ergodic measures with their measure theoretic entropy.  As an application we obtain a criterion for the existence of measure of maximal entropy for geometrically finite manifolds due to Dalbo, Otal and Peigne. Our method has the advantage to also cover nonpositively curved manifolds with certain properties. Part of this talk is based on joint work with F. Riquelme.
Sala 1
2017-06-16
16hrs.
Coloquio de Matemática UC
Marcelo Arenas. PUC
P versus NP
Abstract:
En esta charla se explicará el problema del milenio P versus NP, poniendo especial énfasis en la definición de los conceptos necesarios para entender este problema de ciencia de la computación desde el punto de vista de la matemática.
Sala 2
2017-06-16
17:00hrs.
Seminario de Pregrado en Matemáticas
Sebastián Pavez. PUC
Conjuntos de Vitali
Abstract:
Vamos a discutir como definir la noción de tamaño de un conjunto en la recta real. Con esto construiremos un conjunto al cual no le podemos asignar una noción de tamaño intuitiva. Discutiremos porque este tipo de conjuntos existe y falla esta definición de tamaño.
Sala 2
2017-06-16
14:30hrs.
Seminario de Geometría Algebraica
Sukhendu Mehrotra. PUC Chile
Exceptional Bundles From Surface Degenerations II
sala 2
2017-06-15
15:30hrs.
Seminario de Probabilidad
Ciprian Tudor. Lille
A link between the zeta function and stochastic calculus
Abstract:
 The study of the zeros of the Riemann zeta function constitutes one of the most challenging problems in mathematics. A large literature in devoted to the study of the behavior of the zeta zeros. We will  discuss  how  tools from stochastic analysis, and in particular from Malliavin calculus (multiple integrals,  Wiener chaos, Stein method etc) can be used in the study of some aspects of the behavior of  the zeta function.
Seminarios John Von Neumann CMM, ubicada en Beauchef 851, Torre Norte, Piso 7 (ingreso ascensores torre poniente)
2017-06-15
17:00hrs.
Seminario de Postgrado en Matemáticas
Anibal Velozo. Universidad de Princeton
Topología, geometría y dinámica en dimensiones bajas.
Abstract:
En esta charla explicaré resultados conocidos para superficies de Riemann que relacionan aspectos geométricos y dinámicos. Luego nos centraremos en discutir que se ha hecho en dimensiones más grandes. Terminaremos la charla con algunas preguntas abiertas.
Sala 3, Facultad de Matemáticas
2017-06-13
14:00hrs.
Estadística Educacional
Rodrigo Vargas. Pontificia Universidad Catolica de Chile
Relación entre medios y Espacios de Aprendizaje
Abstract:
Un "medio" es una colección de transformaciones en un conjunto de estados, especificados por dos axiomas restrictivos. La charla se centra en la relación entre colecciones bien clasificadas (en particular, Espacios de aprendizaje) y los medios. Describiremos algunos de ellos en nuestra primera sesión. Luego daremos las definiciones básicas y los dos axiomas que definen un medio.

Sala 2
2017-06-13
16:00hrs.
Seminario de Probabilidad
Milica Tomacevic. Tosca Team, Inria Sophia-Antipolis Mediterranee
A new probabilistic interpretation of Keller-Segel model for chemotaxis, application to 1-d.
Abstract:
The Keller Segel (KS) model for chemotaxis is a two-dimensional system of parabolic or elliptic PDEs. Motivated by the study of the fully parabolic model using probabilistic methods, we give rise to a non-linear SDE of McKean-Vlasov type with a highly non standard and singular interaction kernel.
In this talk I will briefly introduce the KS model, point out some of the PDE analysis results related to the model and then, in detail, analyze our probabilistic interpretation in the case d=1.
This is a joint work with Denis Talay (TOSCA team, INRIA Sophia-Antipolis Mediterranee).
Sala John Von Neumann, 7mo piso, CMM, U. Chilehttp://nm.cmm.uchile.cl/seminarios/
2017-06-09
14:30hrs.
Seminario de Geometría Algebraica
Sukhendu Mehrotra. PUC Chile
Exceptional bundles from surface degenerations I
sala 2
2017-06-09
12:00 hrs.
Seminario de Estadística
Ricardo Bórquez. Departamento de Economía Agraria, Facultad de Agronomía e Ingeniería Forestal
Financial Markets: Controversial or Untestable Theories?
Abstract:

This paper demonstrates a measurability property of no-arbitrage prices, which precludes martingale law identification based on price information. Theoretical model hypotheses defined on martingale laws  are therefore untestable using prices. Examples of such untestable models are  found in the  literature of rational  bubbles, efficient  markets, and more  recently, of arbitrage pricing.


Sala 2, Facultad de Matemáticas
2017-06-06
16:00hrs.
Seminario de Análisis y Geometría
Pilar Herreros. PUC
Mediatrices en superficies
Abstract:
Dados dos puntos en una superficie Riemanniana llamamos mediatriz al conjunto de puntos equidistante a ambos puntos dados.
Hablaremos de la estructura que tiene este conjunto y de su regularidad,  en particular de que sus vertices son radialmente linearizables.  
 

Sala 2, Facultad de Matemática
2017-06-02
12:00hrs.
Seminario de Estadística
Mauricio Castro. Universidad de Concepción
Recent advances in censored regression models
Abstract:

Recently, the study of statistical models where the dependent variable is censored has been studied in different fields, namely, econometric analysis, clinical assays and biostatistical analysis among others. In practice, it is quite common assume Gaussianity for the random components of the model due mainly to the computational flexibility for parameter estimation.

However, such an assumption may not be realistic. In fact, the likelihood-based and Bayesian inferences for censored models can be seriously affected by the presence of atypical observations, skewness and/or the misspecification of the distributions for random terms.

The objective of this talk is to provide a review about statistical models for censored data using non-Gaussian families of distributions to model human immunodeficiency virus (HIV) dynamics. 


Sala 2, Facultad de Matemáticas
2017-06-02
16:00hrs.
Coloquio de Matemática UC
Katia Vogt. Universidad Adolfo Ibañez
Las matemáticas en la lucha contra enfermedades infecciosas
Abstract:
La Epidemiología Matemática ha ido adquiriendo fuerza a través del tiempo, y en la actualidad el análisis y modelamiento matemático es clave en el estudio de la propagación de enfermedades infecciosas. Miraremos algunos ejemplos de cómo un proceso de trasmisión de enfermedades puede ser representado matemáticamente mediante modelos determinísticos de ecuaciones diferenciales, por ejemplo, vía modelos del tipo SIR. Además, discutiremos de qué forma esta representación matemática puede ser utilizada para estudiar, entender y/o controlar la dinámica de una enfermedad en una población. Modelos matemáticos pueden ser de gran ayuda para la toma de decisiones en salud pública, por ejemplo, al ser capaces de orientar la forma de implementación de medidas de control de una enfermedad. En particular, entenderemos durante la charla la importancia del parámetro epidemiológico "Número reproductivo"; cómo éste afecta la dinámica de distintos modelos matemáticos, y de qué forma nos explica la agresividad y/o capacidad de invasión de la enfermedad estudiada.
Sala 2, Facultad de Matemáticas
2017-06-02
14:30hrs.
Seminario de Geometría Algebraica
José Yáñez. PUC Chile
puntos de acumulación de K^2 en superficies estables
sala 2, Facultad de Matemáticas PUC
2017-05-31
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Karim Pichara. PUC
Data Science for Astronomy
Abstract:
In the last few years, there has been an increased interest towards computer applications for astronomical research. This interest is mainly triggered by the ongoing and future observational projects expected to deliver huge amounts of high-quality data, which needs to be promptly analyzed. Some illustrative examples are: the upcoming Large Synoptic Survey Telescope (LSST), the ongoing Vista Variables in the Via Láctea (VVV) ESO Public Survey, and the Atacama Large Millimeter/submillimeter Array (ALMA), among others. Besides the upcoming telescopes, today we have hundreds of astronomical catalogs of tens of millions of objects, available online. All this information makes the Astronomical analysis of stellar objects impossible without the help of computer systems. Last advances in data science, Machine Learning, and Statistics offer us very powerful solutions to explore Astronomical data, nevertheless, there are many challenges that we still need to overcome. In this talk I will present a summary of our main work in time series automatic classification, light-curve representation, automatic detection of specific types of stars, discovery of unknown classes of stellar objects and meta models for efficient and automatic integration of trained experts. 
Auditorio Nisnolav Bralic
2017-05-30
16:00hrs.
Seminario de Análisis y Geometría
Monica Musso. PUC
Existence, Compactness and Non Compactness for fractional Yamabe Problem
Abstract:
 Let $(X^{n+1}, g^+)$ be an $(n+1)$-dimensional asymptotically hyperbolic manifold with a conformal infinity $(M^n, [h])$. The fractional Yamabe problem consists in finding a metric in the conformal class $[h]$ whose fractional scalar curvature is constant.
In this talk, I will present some recent results concerning existence of solutions to the fractional Yamabe problem,  and also properties of compactness and non compactness of its solution set, in comparison with what is known in the classical case.
These results are in collaboration with Seunghyeok Kim and Juncheng Wei.
Sala 2, Facultad de Matemática
2017-05-26
12:00 hrshrs.
Seminario de Estadística
Nedret Billor. Department Of Mathematics And Statistics Auburn University
Robust Inference in Functional Data Analysis
Abstract:

In the last twenty years, a substantial amount of attention has been drawn to the field of functional data analysis. While the study of the probabilistic tools for infinite dimensional variables started in the beginning of the 20th century, the development of statistical models and methods for functional data has only really been developed in the last two decades since many scientific fields involving applied statistics have started measuring and recording massive continuous data due to rapid technological advancements. The methods developed in this field mainly require homogeneity of functional data, namely free of outliers. However, the development of methods in the presence of outliers has just been recently studied. In this talk, we focus on the effect of outliers on functional data analysis techniques. Then we introduce robust estimation and variable selection methods for a special functional regression model as well as simultaneous confidence band for the Mean Function of functional data. Simulation studies and data applications are presented to compare the performance of the proposed methods with the non?robust techniques. 


Sala 2, Facultad de Matemáticas
2017-05-26
14:30hrs.
Seminario de Geometría Algebraica
Sergio Troncoso. PUC Chile
Theory of Peeling
sala 2
2017-05-24
14.30hrs.
Seminario de Postgrado en Estadística
Gabriel Muñoz. Estudiante, Doctorado Estadística UC
Modelos estadísticos en educación: Modelos Rasch y Espacios de conocimiento, parámetros de interés y parámetros identificados
Abstract:
Los modelos Rash han sido ampliamente estudiados y constantemente actualizados a través de la incorporación de nuevos parámetros, tanto en sus versiones de efectos fijos como aleatorios. Por otro lado, la incorporación de modelos estadísticos en Espacios de conocimiento, probablemente no ha gozado de protagonismo que, desde mi punto de vista, merecen. En esta charla se hará una breve explicación de los parámetros de interés y los parámetros identificados de modelos tipo Rasch y modelos estadísticos en Espacios de conocimiento.
Sala 3, Facultad de Matemática UC
2017-05-23
16:00hrs.
Seminario de Análisis y Geometría
Duvan Henao. PUC
Biaxiality in liquid crystals at low temperatures
Abstract:
I will present a joint work with Apala Majumdar and Adriano Pisante where we study the Nobel-winner Landau-de Gennes functional for nematic liquid crystals. We identify the location of defects in the low temperature limit and show the coexistence of biaxial and negative uniaxial points around each defect. We also estimate the size of the biaxial regions.
Sala 2, Facultad de Matemática
2017-05-22
16:30hrs.
Seminario de Sistemas Dinámicos
Jaqueline Siqueira. Puc-Rio
Equilibrium states of partially hyperbolic horseshoes: uniqueness and statistical properties.
Abstract:
We prove uniqueness of equilibrium states of partially hyperbolic horseshoes associated to Holder continuous potentials with small variation. (Joint  work with Isabel Rios). In order to derive some statistical properties for the unique equilibrium state  we define a projection map associated to the horseshoe and prove a spectral gap for its transfer operator acting on the space of Holder continuous observables. From this we deduce an exponential decay of correlations and a central limit theorem. Finally, we extend these results to the horseshoe. ( Joint work with Vanessa Ramos).
Sala 1
2017-05-19
14:30-16:00hrs.
Seminario de Geometría Algebraica
Sönke Rollenske. U Marburg
Geometry of Stable Surfaces III
Sala 2, Facultad de Matemática
2017-05-19
16hrs.
Coloquio de Matemática UC
Jan Kiwi. PUC
Dinámica de polinomios cúbicos e irreducibilidad
Abstract:
El espacio de polinomios cúbicos complejos en una variable vistos como sistemas dinámicos es isomorfo a $\mathbb{C}^2$. Este espacio ha sido intensamente estudiado desde fines de los 80. Una de las estrategias ha sido estudiar ciertos subconjuntos algebraicos de dimensión compleja $1$ donde un mayor arsenal de técnicas está a nuestra disposición. La familia mas notable de tales subconjuntos es $\{ \mathcal{S}_n \}$ donde $n$ es  natural y $\mathcal{S}_n$ es el conjunto formado por polinomios con un punto crítico de periódo exactamente $n$. En 1992 Milnor preguntó si $\mathcal{S}_n$ es irreducible (equivalentemente conexo) para todo $n$. En la charla presentaremos un trabajo reciente en que respondemos está pregunta en forma afirmativa
(trabajo conjunto con Matthieu Arfeux, Pontificia Universidad Católica de Valparaiso).

Sala 2
2017-05-19
12:00 hrs.
Seminario de Estadística
Isabelle Beaudry. Pontificia Universidad Católica de Chile
Correcting for nonrandom recruitment with RDS data: design-based and Bayesian approaches
Abstract:

Respondent-driven sampling (RDS) is a sampling mechanism that has proven very effective to sample hard-to-reach human populations connected through social networks. A small number of individuals typically known to the researcher are initially sampled and asked to recruit a small fixed number of their contacts who are also members of the target population. Each subsequent sampling waves are produced by peer recruitment until a desired sample size is achieved. However, the researcher's lack of control over the sampling process has posed several challenges to producing valid statistical inference from RDS data. For instance, participants are generally assumed to recruit completely at random among their contacts despite the growing empirical evidence that suggests otherwise and the substantial sensitivity of most RDS estimators to this assumption. The main contributions of this study are to parameterize alternative recruitment behaviors and propose a design-based and a model-based (Bayesian) estimators to correct for nonrandom recruitment.


Sala 2, Facultad de Matemáticas
2017-05-18
17:00hrs.
Seminario de Teoría Espectral
Silvius Klein . PUC Rio de Janeiro
Anderson localization for one-frequency quasi-periodic block Jacobi operators
Abstract:
Consider a one-frequency, quasi-periodic, block Jacobi operator, whose blocks are generic matrix-valued analytic functions. This model is a natural generalization of Schroedinger operators of this kind. It contains all finite range hopping Schroedinger operators on integer or band integer lattices.
In this talk I will discuss a recent result concerning Anderson localization for this type of operator under the assumption that the coupling constant is large enough but independent of the frequency.
Sala 1
2017-05-17
14:30hrs.
Seminario Agco
Carlos Ochoa. U Chile
Synergistic Solutions on MultiSets
Abstract:
Karp et al. (1988) described Deferred Data Structures for Multisets as "lazy" data structures which partially sort data to support online rank and select queries, with the minimum amount of work in the worst case over instances of size $n$ and number of queries $q$ fixed. Barbay et al. (2016) refined this approach to take advantage of the gaps between the positions hit by the queries (i.e., the structure in the queries). We develop new techniques in order to further refine this approach and take advantage all at once of the structure (i.e., the multiplicities of the elements), some notions of local order (i.e., the number and sizes of runs) and global order (i.e., the number and positions of existing pivots) in the input; and of the structure and order in the sequence of queries. Our main result is a synergistic deferred data structure which outperforms all solutions in the comparison model that take advantage of only a subset of these features. As intermediate results, we describe two new synergistic sorting algorithms, which take advantage of some notions of structure and order (local and global) in the input, improving upon previous results which take advantage only of the structure (Munro and Spira 1979) or of the local order (Takaoka 1997) in the input; and one new multiselection algorithm which takes advantage of not only the order and structure in the input, but also of the structure in the queries.
Av República 779 B (Beauchef), Sala 3er Piso.
2017-05-17
11:30hrs.
Estadística Educacional
Rodrigo Vargas. Pontificia Universidad Católica de Chile
Construcción de un KS a partir de otros más pequeños
Abstract:
Resumen:
Discutiremos la construcción teórica de una estructura de conocimiento combinando un número finito estructuras de conocimiento más pequeñas. Estas estructuras que están definidas en un subdominio pueden ser consideradas como proyecciones de una estructura desconocida en el dominio completo. Mostraremos los resultados principales que permiten tal construcción, estudiando como se conservan las propiedades de las estructuras mas pequeñas por la construcción.

Sala 3 Facultad de Matemáticas
2017-05-17
14:30hrs.
Seminario de Ingeniería Matemática y Computacional
Marc Schroder. U Chile
Network Pricing: How to Induce Optimal Flows Under Strategic Link Operators
Abstract:
Network pricing games provide a framework for modeling real-world settings with two types of strategic agents: users of the network and owners (operators) of the network. Owners of the network post a price for usage of the link they own; users of the network select routes based on price and level of use by other users. The challenge in these games is that there are two levels of competition: one, among the owners to attract users to their link so as to maximize profit; and second, among users of the network to select routes that are cheap yet not too congested. Interestingly, we observe that: (i) an equilibrium may not exist; (ii) it might not be unique; and (iii) the network performance at equilibrium can be arbitrarily inefficient. Our main result is to observe that a slight regulation on the network owners market solves all three issues above. Specifically, if the authority could set appropriate caps (upper bounds) on the tolls (prices) operators can charge then: the game among the link operators has a unique strong Nash equilibrium and the users’ game results in a Wardrop equilibrium that achieves the optimal total delay. We call any price vector with these properties a great set of tolls. We then ask, can we compute great tolls that minimize total users’ payments? We show that this optimization problem reduces to a linear program in the case of single-commodity series-parallel networks. Starting from the same linear program, we obtain multiplicative approximation results for arbitrary networks with polynomial latencies of bounded degree, while in the single-commodity case we obtain a surprising bound, which only depends on the topology of the network. 
Auditorio San Agustín
2017-05-15
16:30hrs.
Seminario de Sistemas Dinámicos
Robin Tucker-Drob. Texas A&m University
Inner amenable groupoids and compact actions
Abstract:
We introduce the notion of inner amenability for discrete p.m.p. (=probability measure preserving) groupoids which generalizes the notion of inner amenability of groups. In the special case of of p.m.p. equivalence relations, this gives a new orbit equivalence invariant. We show that the orbit equivalence relation associated to any free compact action of an inner amenable group is itself inner amenable as a groupoid. Conversely, any group which freely generates an inner amenable p.m.p. equivalence relation must itself be inner amenable.
Sala J. Neumann, CMM
2017-05-12
16:00 - 17:00hrs.
Seminario de Geometría Algebraica
Sönke Rollenske. U Marburg
Geometry of Stable Surfaces II
Sala 2, Facultad de Matemáticas
2017-05-12
14:30-15:45hrs.
Seminario de Geometría Algebraica
Sönke Rollenske. U Marburg
Geometry of Stable Surfaces I
Abstract:
Stable surfaces are the two-dimensional analogue of stable curves: they are
the singular surfaces that are parametrised by a natural compactification of
the Giesecker moduli space of surfaces of general type.
In the lectures I will illustrate some basic techniques needed to deal with
such surfaces. We will see that any closer look at examples quickly takes us
to classical questions in algebraic geometry.
Sala 2, Facultad de Matemáticas
2017-05-10
14.30hrs.
Seminario de Postgrado en Estadística
Francisca Calderón. Estudiante, Doctorado Estadística UC
Análisis psicométrico de instrumentos de medición de variables latentes. Caso: ?Test habilidades cognitivas? enfoque clásico y teoría de respuesta al ítem con implementación en software R
Abstract:

Se presenta el estudio y análisis psicométrico de un instrumento  orientado a la medición de las competencias lectoras en nivel NB2 de Enseñanza Básica. En este contexto, se define el objetivo de evaluar las características psicométricas que posee el instrumento. La metodología utilizada para dar cuenta del estudio se basa en dos enfoques complementarios en el área de la psicometría: Teoría clásica de los Test (TCT) y Teoría de Respuesta al Ítem (IRT). Su implementación se realizó mediante el programa estadístico R,  de disposición gratuita. Resultado de esta investigación surgen tanto la validación efectiva del instrumento “Prueba Habilidades Cognitivas” como una experiencia de aplicación práctica que consagra al software R como alternativa eficaz en el tratamiento y análisis de instrumentos de medición de variables latentes, en contraste con el software especializado PARSCALE. Además, se concluye la existencia de alta asociación entre los coeficientes de los ítems y la habilidad de los sujetos, estimados mediante ambos programas computacionales.


Sala 3, Facultad de Matemática UC
2017-05-10
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Norbert Heuer. PUC
Introducción al método DPG, una vista analítica
Abstract:
El acrónomo DPG se refiere al método de Petrov-Galerkin discontinuo con
funciones de test optimales. Se trata de aproximar soluciones de
ecuaciones en derivadas parciales, en particular aquellas que son
perturbadas de manera singular.
En esta charla discutimos qué significa esto. El foco va a ser en
problemas de difusión con reacción dominante. Explicamos qué falla en el
uso de elementos finitos y por qué. Basado en estos resultados
desarrollamos el método DPG para superar los problemas observados.
Ilustramos los resultados teóricos con algunos experimentos numéricos.
Auditorio San Agustín
2017-05-10
11:20hrs.
Estadística Educacional
Gabriel Muñoz. Pontificia Universidad Católica de Chile
Coordinación Seminario 2017 - Contenidos previos y planificación
Abstract:
En esta primera sesión del año, realizaremos un resumen de los contenidos estudiados en las anteriores y se definirán los temas a estudiar y exponer en los próximos seminarios. Se invita a todos quienes quieran incorporarse a este seminario, con interés en Medición Educacional, Psicometría, Matemáticas o Estadística en general, a asistir a esta sesión e incorporarse al grupo asistente y expositor.
Sala 3
2017-05-09
16:00hrs.
Seminario de Análisis y Geometría
Suspendido. PUC
SUSPENDIDO
Sala 2, Facultad de Matemáticas UC
2017-05-08
5:00pmhrs.
Seminario Capde
Erwin Topp Paredes. Universidad de Santiago de Chile
Parabolic equations with Caputo time derivative
Abstract:
In this talk we report results presented in [Topp & Yangari 2017] about well-posedness of fully nonlinear Cauchy problems in which the time derivative is of Caputo type. We address this question in the framework of viscosity solutions, obtaining the existence via Perron’s method, and comparison for bounded sub and supersolutions by a suitable regularization through inf and sup convolution in time. As an application, we prove the steady-state large time behavior in the case of proper nonlinearities and provide a rate of convergence by using the Mittag-Leffler operator.
Sala 2, Facultad de Matemáticas, PUChttp://capde.cl/scientific-activities-2/
2017-05-08
16:30hrs.
Seminario de Sistemas Dinámicos
Tuomas Sahlsten. University Of Bristol
Quantum ergodicity and limit multiplicities
Abstract:
We will give an introduction to the topic of “quantum ergodicity” and review the history and current challenges of the problem. The quantum ergodicity theorem states that on Riemannian surfaces with an ergodic geodesic flow, most eigenfunctions of the Laplacian equidistribute spatially in the large eigenvalue limit. In this talk, we will present an alternative equidistribution theorem for eigenfunctions where the eigenvalues stay bounded and we take instead sequences of compact hyperbolic surfaces that become large in, say, volume. Thus the result combines quantum ergodicity with the theory of limit multiplicities in spectral theory (after DeGeorge and Wallach).

The approach is motivated by the recent works of Anantharaman, Brooks, Le Masson, and Lindenstrauss on eigenvectors of the discrete Laplacian on regular graphs, and the holomorphic form analogues by Nelson, Pitale and Saha. In the dynamics side of the proof we require the exponential mixing structure of the geodesic flow on hyperbolic surfaces, in particular a quantitative mean ergodic theorem by Nevo.

This is a joint work with Etienne Le Masson (Bristol).

Sala 1
2017-05-08
4:00pmhrs.
Seminario Capde
María Medina. Pontificia Universidad Católica de Chile
A mixed fractional problem. Moving the boundary conditions
Abstract:
A natural question when one considers the mixed eigenvalue problem for the Laplacian (zero DIrichlet condition in D and Neumann homogeneous in N where $\Omega$ is a Lipschitz bounded domain in $R^N$ and D, N are disjoint submanifolds of ∂Ω) is whether the configuration of the sets D and N determines the behavior of u. Is it similar to the solution of the Dirichlet problem when N is small? or does it behave like the Neumann eigenfunction when N is large? Several authors have shown results where different configurations of D and N provide very different behaviors of u (see for example [Colorado & Peral 2003, Denzler 1999]) depending on the size of the sets, but also on their location.

In this talk we will try to understand the analogous non local problem where N and D are now two open sets of $R^N\Omega$. As we will see, the fact that the boundary now happens to be the whole $R^N\Omega$ instead of ∂Ω completely changes the possible configurations of the sets (one can even have both sets of unbounded measure). The purpose of this talk will be to understand what “a small boundary set” means here, and to analyze how D and N can move to recover the classical results.

This is a joint work with T. Leonori, I. Peral, A. Primo and F. Soria, that can be found at https://arxiv.org/pdf/1702.07644.pdf.
Sala 2, Facultad de Matemáticas, PUChttp://capde.cl/scientific-activities-2/
2017-05-05
14:30hrs.
Seminario de Geometría Algebraica
Sergio Troncoso. PUC Chile
Descripción del log MMP
Sala 2, Facultad de Matemáticas PUChttp://www.mat.uc.cl/~urzua/
2017-05-05
16hrs.
Coloquio de Matemática UC
Gueorgui Dimitrov Raykov. PUC
Operadores de Pauli con campos magnéticos casi periódicos
Abstract:
Se considerará el operador bidimensional de Pauli H(b) con campo magnético casi periódico b. Se discutirán algunas propiedades ergódicas de H(b). La parte principal de la charla será dedicada al análisis de Ker H(b), en particular en el caso de promedio nulo del campo magnético b.
Sala 2
2017-05-05
15:00 Hrs.hrs.
Seminarios Extraordinarios
M. Lein. Aimr, Japan
Workshop Top Math-? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-05-04
15:00 Hrs.hrs.
Seminarios Extraordinarios
S. Teufel. U. Tübingen, Germany
Workshop Top Math-? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-05-03
15:00 Hrs.hrs.
Seminarios Extraordinarios
Georgui Raikov. Pontificia Universidad Católica de Chile
Workshop Top Math-? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-05-02
15:00 Hrs.hrs.
Seminarios Extraordinarios
Rafael Tiedra. Pontificia Universidad Católica de Chile
Workshop Top Math-? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-05-02
16:00hrs.
Seminario de Análisis y Geometría
Hanne Van Den Bosch. PUC
Spectrum of Dirac operators describing Graphene Quantum dots
Abstract:
Low energy electronic excitations in graphene, a two-dimensional lattice of carbon atoms, are described effectively by a two–dimensional Dirac operator. For a bounded flake of graphene (a quantum dot), the choice of boundary conditions determines various properties of the spectrum. Several of these choices appear in the physics literature on graphene. For a simply connected flake and a family of boundary conditions, we obtain an explicit lower bound on the spectral gap around zero. We can also study the effect of the boundary conditions on eigenvalue sums in the semiclassical limit. This is joint work with Rafael Benguria, Søren Fournais and Edgardo Stockmeyer.
Sala 2, Facultad de Matemáticas UC
2017-04-27
15:00 Hrs.hrs.
Seminarios Extraordinarios
G. Landi. Universidad de Trieste, Italia
Workshop Top Math-? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-04-26
15:00 Hrs.hrs.
Seminarios Extraordinarios
E. Sezgin. U. Texas A&m, Estados Unidos
Workshop Top Math-? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-04-26
14.30hrs.
Seminario de Postgrado en Estadística
Eduardo Alarcón. Estudiante, Doctorado en Estadística UC
Test de hipótesis que verifica la 2da ley generalizada de Chargaff
Sala 3, Facultad de Matemáticas UC
2017-04-25
15:30hrs.
Seminario de Probabilidad
Christophe Profeta. Universite D'evry Val D'essonne
Stable Langevin model with diffusive-reflective boundary conditions. 
Abstract:

Resumen : We consider a one-dimensional stable Langevin process confined in the upper half-plane and submitted to a diffusive-reflective boundary condition whenever the particle position hits 0. We show that different regimes appear according to the value of the chosen parameters. We then use this study to construct the law of a (free) stable Langevin process conditioned to stay positive, thus extending earlier works on the integrated Brownian motion. Such construction finally enables us to improve some recent persistence probability estimates. This is a joint work with Jean-François Jabir.

Sala 5, Facultad de matemáticas, Campus San Joaquín. PUC.http://nm.cmm.uchile.cl/seminarios/
2017-04-25
15:00 Hrs.hrs.
Seminarios Extraordinarios
J. Alfaro. Pontificia Universidad Católica de Chile
Workshop Top Math-? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-04-25
16:00 hrs.
Seminario de Análisis y Geometría
Carmen Cortázar. PUC
Large time behavior of porous medium solutions in exterior domains
Abstract:
Let  $\mathcal{H}\subset \mathbb{R}^N$ be a non-empty bounded open set. We consider the porous medium equation in the complement of  $\mathcal{H}$ ,  with zero Dirichlet data on  its boundary and nonnegative compactly supported integrable initial data.
 
Kamin and Vázquez, in 1991, studied the large time behavior of solutions of such  problem  in space dimension 1.    Gilding and Goncerzewicz, in 2007, studied this same problem  dimension 2.  However, their result does not say much about the behavior when the points  are in the so called near field scale. In particular, it does not give a sharp decay rate, neither a nontrivial asymptotic profile, on compact sets.
In this paper we characterize the large time behavior in such scale, thus completing their results.
 
This a Joint work with Fernando Quiros ( Universidad Autonoma de Madrid, Spain) and Noemí Wolanski ( Universidad de Buenos Aires, Argentina).
 

Sala 2, Facultad de Matemáticas UC
2017-04-24
15:00 Hrs.hrs.
Seminarios Extraordinarios
Y. Schroder. Ubb, Chile
Workshop Top Math- ? (Plenary lecture)
Auditorio Ninoslav Bralic - Facultad de Matemáticas - Pontificia Universidad Católica de Chile
2017-04-24
16:30hrs.
Seminario de Sistemas Dinámicos
Godofredo Iommi. Puc-Chile
Termodinámica de la transformación de Jacobi-Perron
Abstract:
El algoritmo de Jacobi-Perron provee aproximaciones simultáneas a dos números reales por racionales con denominadores comunes. En esta charla discutiré cómo una variante del formalismo termodinámico no aditivo (desarrollado conjuntamente con Yuki Yayama) permite estudiar la calidad de dichas aproximaciones. Este es parte de un trabajo en desarrollo realizado en conjunto con Jairo Bochi y Pablo Shmerkin.
Sala 1, Fac Mates, PUC
2017-04-21
16hrs.
Coloquio de Matemática UC
Christian Sadel. PUC
Sobre los operadores aleatorios
Abstract:
Random operators such as the Anderson model have been introduced and widely studied by physicists to model the quantum mechanics in disordered systems, such as doped semi-conductors and imperfect crystals. We will give some overview of the theory on random operators and state some more recent results and also discuss some open conjectures
Sala 2
2017-04-21
12:00hrs.
Seminario de Estadística
Felipe Osorio. Instituto de Estadística, Pontificia Universidad Católica de Valparaíso
Test Gradiente Para Extremum Estimators
Abstract:

En este trabajo se introduce el test gradiente propuesto por Terrell [Comp. Sci. Stat. 34: 206-215, 2002] al contexto de estimadores que surgen como el extremo de una función objetivo, esta clase general de estimadores frecuentemente conocidos como “extremum estimators” proveen un marco general para el estudio de distintos procedimientos de estimación que comparten principios comunes. En esta charla, nos enfocamos principalmente en abordar test de hipótesis no lineales así como de la aplicación del test gradiente en diagnóstico de influencia. La metodología es aplicada para determinar la igualdad entre razones de Sharpe asociado a las rentabilidades de los fondos de pensiones desde el sistema previsional chileno. 


Sala 2, Facultad de Matemáticas
2017-04-21
14:30hrs.
Seminario de Geometría Algebraica
Sergio Troncoso. PUC
Ejecutando MMP explícitamente y su resultado final
Sala 2 (Facultad de Matemáticas PUC)
2017-04-18
16:00hrs.
Seminario de Análisis y Geometría
Abraham Solar. PUC
Stability of semi-wavefronts for delayed reaction-diffusion equations
Abstract:
Semi-wavefronts are bounded positive solutions of delayed
reaction-diffusion equations such that its shape is not changed in the
time and they move with constant speed en the time. In this talk I
will show the most important results about stability of this solutions
and how they determinate the propagation speed of the a broad class of
solutions.
Sala 2, Facultad de Matemáticas UC
2017-04-17
16hrs.
Seminario de Sistemas Dinámicos
Arnaldo Nogueira. Inst. Mat. Marseille
Topological Dynamics of piecewise \Lambda-affine maps of the interval
Abstract:
Let 0 < a < 1, 0 ≤ b < 1 and I = [0,1). We call contracted rotation the interval map φa,b : x  I  ax+b mod1. Once a is fixed, we are interested in the dynamics of the one-parameter family φa,b, where b runs on the interval interval [0, 1). Any contracted rotation has a rotation number ρa,b which describes the asymptotic behavior of φa,b. In the first part of the talk, we analyze the numerical relation between the parameters a, b and ρa,b and discuss some applications of the map φa,b. Next, we introduce a generalization of contracted rotations. Let −1 < λ < 1 and f : [0, 1)  R be a piecewise λ-affine contraction, that is, there exist points 0 = c0 < c1 < ··· < cn−1 < cn = 1 and real numbers b1,...,bn such that f(x) = λx + bi for every x [ci−1,ci). We prove that, for Lebesgue almost every δ  R, the map fδ = f + δ (mod 1) is asymptotically periodic. More precisely, fδ has at most n + 1 periodic orbits and the ω-limit set of every x  [0, 1) is a periodic orbit. 
Sala J. Neumann CMM
2017-04-12
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Irina Pettersson. The Artic University Of Norway
Existence and uniqueness results for convection-diffusion equation in unbounded domains
Abstract:
We study the existence and uniqueness of a bounded solution to a stationary convection-diffusion equation in semi-infinite and infinite cylindrical domains. The operator is not self-adjoint, and depending on the direction of the effective convection we either get a unique solution, a family of solutions or even non-existence. 
Auditorio San Agustín
2017-04-12
14:30hrs.
Seminario Agco
Marc Schroder. U Chile
Claim games for estate division problems
Abstract:

The estate division problem, also known as bankruptcy problem, concerns the issue of dividing an estate among a group of claimants when the sum of entitlements exceeds the size of the estate. This problem was formally introduced by O’Neill (1982), after which most of the literature focused on comparing different solution rules by means of their properties. We approach the problem strategically and analyse the claim game.

 

Republica 779B, Sala P3, 3rd floor.
2017-04-10
16:00hrs.
Seminario de Sistemas Dinámicos
Sebastian Donoso. Universidad O'higgins
Quantitative multiple recurrence for two and three transformations.
Abstract:
In this talk I will provide some counter examples for quantitative multiple recurrence problems for systems with more than one transformation.  For instance, I will show that there exists an ergodic system $(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that 
\[ \mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell} \] 
for every $n \in \mathbb{N}$. 
The construction of such a system is based on the study of ``big'' subsets of $\mathbb{N}^2$ and $\mathbb{N}^3$  satisfying combinatorial properties.
 
This a joint work with Wenbo Sun.

Sala J. Neumann, CMM
2017-04-07
16hrs.
Coloquio de Matemática UC
Nikola Kamburov. PUC
Free Boundaries and Minimal Surfaces
Abstract:
A free boundary is an interface between two materials like oil and water. Remarkably, its mathematics echoes that used to describe soap films, i.e. the mathematics of minimal surfaces. A prominent theme in the classical theory of minimal surfaces is the study of how a prescribed topology imposes rigidity on the shape of such surfaces. In this talk I will describe the connection between the two fields and discuss some analogous results in the free boundary setting.
Sala 2
2017-04-07
14:30hrs.
Seminario de Geometría Algebraica
José Ignacio Yáñez. PUC
Pares log canonical y teorema del Cono
Sala 2 PUC
2017-04-06
17:00hrs.
Seminario de Teoría Espectral
Sébastien Breteaux . Basque Center For Applied Mathematics
The Time-Dependent Hartree-Fock-Bogoliubov Equations for Bosons
Abstract:
Joint work with V. Bach, T. Chen, J. Fröhlich, and I. M. Sigal.

It was first predicted in 1925 by Einstein (generalizing a previous work of Bose) that, at very low temperatures, identical Bosons could occupy the same state. This large assembly of Bosons would then form a quantum state of the matter which could be observed at the macroscopic scale. The first experimental realisation of a gas condensate was then done in 1995 by Cornell and Wieman, and this motivated numerous works on Bose-Einstein condensation.

In particular, we are interested in the dynamics of such a condensate. To describe the dynamics of such a condensate, the first approximation is the time dependent Gross-Pitaevskii equation, or, in an other scaling, the Hartree equation. To precise this description, we derive the time-dependent Hartree-Fock-Bogoliubov equations describing the dynamics of quantum fluctuations around a Bose-Einstein condensate via quasifree reduction. We prove global well posedness for the HFB equations for sufficiently regular interaction potentials. We show that the HFB equations have a symplectic structure and a structure similar to an Hamiltonian structure, which is sufficient to prove the conservation of the energy.
Sala 1
2017-04-04
16:00hrs.
Seminario de Análisis y Geometría
Erwan Hingant. Universidad del Bio-Bio
The Stochastic Becker-Döring System
Abstract:
The Becker-Döring equations might be "one of the simplest kinetic model to describe a number of issues in the dynamics of fase transitions", Penrose (1989). This model describes the evolution of the concentration of clusters (or aggregates) according to their size. The rules are simple, a cluster of size $i$ may encounter a particle (cluster of size $1$) to form a new one of size $i+1$. Conversely, a cluster of size $i$ could release a particle leading to a cluster of size $i-1$. In this talk we will present the stochastic version of this rules when the system consists in a finite number of particles, namely a pure jump Markov process on a finite state space. And we will discuss about some results and issues around the law of large number associate to this problem. 

Ref.: E. Hingant and R. Yvinec, Deterministic and Stochastic Becker-Döring equations: Past and Recent Mathematical Developments, Preprint arXiv:1609.00697, 2016.
Sala 2, Facultad de Matemáticas UC
2017-03-31
14:30hrs.
Seminario de Geometría Algebraica
José Ignacio Yáñez. PUC
Introducción al Minimal Model Program
Abstract:
Este semestre estudiaremos el Minimal Model Program (o teoría de Mori) para superficies algebraicas con borde. El objetivo principal es entender la demostración del teorema de boundedness dada por Alexeev a comienzos de los 90s. Este teorema implica que la compactificación del espacio de moduli de superficies algebraicas de tipo general, dada por Kollár y Shepherd-Barron y generalización de la compactificación de Deligne-Mumford para curvas, define una variedad proyectiva. En particular, las singularidades de las correspondientes superficies están acotadas a través de los números de Chern (de hecho  K^2 basta), formando una lista finita. ¿Cuál es esa lista para K^2 dado?

La idea es desarrollar todos los prerequicitos para poder entender los detalles de la demostración.

En esta charla se definirán superficies con bordes, las singularidades involucradas junto a sus discrepancias, el teorema del cono, y todo aspecto básico relacionado con MMP.
Sala 2
2017-03-29
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Pablo Barcelo. U Chile
Querying graph databases
Abstract:
Graph databases have gained renewed interest in the last years, due to their applications in areas such as the Semantic Web and Social Networks Analysis. We study the problem of querying graph databases, and, in particular, the expressiveness and complexity of evaluation for several general-purpose navigational query languages, such as the regular path queries and its extensions with conjunctions and inverses. We distinguish between two semantics for these languages. The ?rst one, based on simple paths, easily leads to intractability in data complexity, while the second one, based on arbitrary paths, allows tractable evaluation for an expressive family of languages.
We also study two recent extensions of these languages that have been motivated by modern applications of graph databases. The ?rst one allows to treat paths as ?rst-class citizens, while the second one permits to express queries that combine the topology of the graph with its underlying data.
Sala Seminario San Agustín, Campus San Joaquín
2017-03-29
14:30hrs.
Seminario Agco
Kevin Schewior. U Chile / Max Planck Institute For Informatics
Chasing Convex Bodies
U Chile, Campus Beauchef, República 779 B, Sala 3er Piso
2017-03-28
16:00hrs.
Seminario de Análisis y Geometría
Sophia Jahns . Tübingen University, Germany
Trapped Light in Stationary Spacetimes
Abstract:
Light can circle a massive object (like a black hole or a neutron star) at a "fixed distance", or, more generally, circle the object without falling in or escaping to infinity. This phenomenon is called trapping of light and well understood in static, asymptotically flat (AF) spacetimes. If we drop the requirement of staticity, similar behavior of light is known, but there is no definiton of trapping available. We present some known results about trapping  of light in static AF spacetimes. Using the Kerr spacetime as a model, we then show how trapping can be better understood in the framework of phase space and work towards a definition for photon regions in stationary AF spacetimes. 

Sala 2, Facultad de Matemáticas UC
2017-03-24
16.30hrs.
Coloquio de Matemática UC
Jan Felipe Van Diejen. Universidad de Talca
Bispectralidad y sistemas de partículas cuánticas integrables
Abstract:
En 1985 Duistermaat y Grünbaum introdujeron el concepto del llamado "problema bispectral". En breve, un problema espectral se llama bispectral si la función propia satisface además una ecuación diferencial lineal en el parámetro espectral. En esta charla explicaremos como la noción de bispectralidad nos provee de una herramienta poderosa en el estudio de las funciones propias de sistemas de partículas cuánticas integrables.
Sala 2
2017-03-24
14:30hrs.
Seminario de Geometría Algebraica
Fabien Trihan. U Sophia, Japón
Abelian varieties over function fields and related conjecture
Abstract:
We will talk about abelian varieties over function fields of positive characteristic and conjectures related to those such as the Birch-Swinnerton-Dyer, the equivariant Tamagawa number conjecture or the Iwasawa Main conjectures

sala 2
2017-03-23
17:00hrs.
Seminario de Teoría Espectral
Rafael Tiedra de Aldecoa. Facultad de Matemáticas, PUC
Spectral analysis of quantum walks with an anisotropic coin
Abstract:
We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we determine the essential spectrum of U, we show the existence of locally U-smooth operators, we prove the discreteness of the eigenvalues of U outside the thresholds, and we prove the absence of singular continuous spectrum for U. Our analysis is based on new commutator methods for unitary operators in a two-Hilbert spaces setting, which are of independent interest.

This is a joint work with Serge Richard (Nagoya University) and Akito Suzuki (Shinshu University).
Sala 1
2017-03-22
14:30hrs.
Seminario Agco
Krzysztof Fleszar. U Chile
Maximum Disjoint Paths: New Algorithms based on Tree-Likeness
Abstract:

Maximum Edge Disjoint Paths is a classical NP-hard problem of finding a
maximum-size subset from a given set of k terminal pairs that can be
routed via edge-disjoint paths.
One of the big open problems in approximation algorithms is to close the
gap between the best known approximation upper bound of $\sqrt{n}$
(Chekuri et al. (2006)) and the best known lower bound of $2^{\sqrt{\log
n}}$ (Chuzhoy et al. (2016)). In their seminal paper, Raghavan and
Thompson (Combinatorica, 1987) introduce the technique of randomized
rounding for LPs; their technique gives an O(1)-approximation when edges
may be used by $O(\log n / \log\log n)$ paths.

In this talk, I introduce the problem and present two of our algorithms
(ESA 2016) that strengthen the fundamental results above. They provide
new bounds formulated in terms of the feedback vertex set number r of a
graph, which measures its vertex deletion distance to a forest.

- An $O(\sqrt{r} \log{kr})}$-approximation algorithm. Up to a
logarithmic factor, it strengthens the best known ratio $\sqrt{n}$ due
to Chekuri et al., as $r \le n$.

- An $O(1)$-approximation algorithm with congestion bounded by
$O(\log{kr} / \log\log{kr})$, strengthening the bound obtained by the
classic approach of Raghavan and Thompson.

At the end, an open problem will be stated.


República 779 B, Sala 3er Piso (Beauchef)
2017-03-21
16:00hrs.
Seminario de Análisis y Geometría
Mauricio Bogoya. Universidad Nacional de Colombia, Bogota
A NON-LOCAL DIFFUSION COUPLED SYSTEM EQUATIONS IN A BOUNDED DOMAIN
Sala 2, Facultad de Matemáticas UC
2017-03-16
17:00hrs.
Seminario de Teoría Espectral
Hermann Schulz-Baldes. Universidad de Erlangen, Alemania
Finite volume calculation of topological invariants
Abstract:
Odd index pairings of K1-group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a lattice, it is shown how to calculate the resulting index as the signature of a suitably constructed finite-dimensional matrix, more precisely the finite volume restriction of the so-called Bott operator. The index is also equal to the eta-invariant of the Bott operator. In presence of real symmetries, secondary $Z_2$-invariants can be obtained as the sign of the Pfaffian of the Bott operator. These results reconcile two complementary approaches to invariants in topological insulators. Joint work with Terry Loring.
Sala 1
2017-03-15
14:30hrs.
Seminario Agco
Saeed Hadikanlo. Univ. de Paris 9
Learning in NonAtomic Anonymous Games: Application to First Order Mean Field Games
Abstract:
We introduce a model of anonymous games where the actions are chosen from possibly player dependent sets. We propose several learning procedures similar to the well-known Fictitious Play and Online Mirror Descent and prove their convergence to equilibrium under the classical monotonicity condition. Typical examples are First Order Mean Field Games.
República 779 B, Sala 3er Piso.
2017-03-14
16:00hrs.
Seminario de Análisis y Geometría
Marcos de la Oliva. Universidad Autónoma de Madrid
Relaxation of a model for nematic elastomers
Abstract:
The direct method of the calculus of variations to find minimizers is based on compactness and lower semicontinuity of the energy functional. In the absence of lower semicontinuity, one option is to find the relaxation, i.e., the largest lower semicontinuous functional below a given one. In nonlinear elasticity, computing the relaxation is difficult beacuse of the non-standard growth conditions. In this talk we show that the relaxation for a model in nonlinear elasticity is given by the quasiconvexification of the integrand. We also propose a model for nematic elastomers (a kind of liquid crystals) in which the energy has a part in the reference configuration and a part in the deformed configuration. We show again that the relaxation is given by the quasiconvexification.
Sala 2, Facultad de Matemáticas UC
2017-03-13
17:00hrs.
Seminario de Sistemas Dinámicos
Tanya Firsova. Kansas State University
Deformation spaces of rational functions
Abstract:
A celebrated Theorem of W.Thurston gives a topological condition when a postcritically finite branched cover can be realized by a rational map. A.Epstein, building on the work of Thurston, studied the spaces of maps constrained by certain postcritically finite relations. He defined deformation spaces for such maps that live in certain Teichmuller spaces. Epstein proved transversality results in holomorphic dynamics using deformation spaces. 
We will discuss how these deformation spaces relate to the ones studied by Mary Rees. We will also discuss topological properties of the Epstein's deformation spaces and give a sufficient condition that guarantees that a given deformation space is not contractible. This is a joint work with J. Kahn and N. Selinger.

Sala 1, Fac. Mates, PUC
2017-03-13
16:00hrs.
Seminario de Sistemas Dinámicos
Mao Shinoda. Keio University
The existence of a dense subset of uncountably maximized continuous functions
Abstract:
The main purpose of the ergodic optimization is to single out invariant measures which maximize the space average of a performance function on a dynamical system.
We mainly consider a dynamical system defined by a continuous self-map on a compact metric space.
There is a major conjecture that for ``many" performance functions there exist unique maximizing measures and the unique measures are supported by a single periodic orbit.
Jenkinson shows that for a generic continuous function there exists unique maximizing measure.
We prove, on the other hand, there exits a dense subset of continuous functions which have uncountably many ergodic maximizing measures.
The main idea of our proof is the application of the Bishop Phelps theorem to the context of maximizing measures.

Sala 1, Fac. Mates, PUC
2017-03-10
16:00hrs.
Seminario de Geometría Algebraica
Dulip Piyaratne. Kavli Ipmu, University Of Tokyo
Stability conditions on derived categories of varieties II
Abstract:
In this talk I will discuss stability conditions on projective threefolds. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for some 3-folds including Fano 3-folds of Picard rank one. However, Schmidt and Martinez gave some counter-examples for Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality in order to get a family of Bridgeland stability conditions, and why it holds for general Fano 3-folds.
Sala 2
2017-03-10
15:00hrs.
Seminario de Geometría Algebraica
Dulip Piyaratne. Kavli Ipmu, University Of Tokyo
Stability conditions on derived categories of varieties
Abstract:
The aim of this talk is to discuss Bridgeland stability conditions on smooth projective varieties. The notion of stability appears in many guises and it is fundamental to geometric invariant theory. There is a systematic way of studying stability conditions due to Bridgeland and his approach is essentially an abstraction of the usual slope stability for sheaves. This categorical stability notion was introduced in order to understand the work of Douglas on Pi-stability in superconformal field theories. However, construction of Bridgeland stability conditions on higher dimensional varieties is a challenging problem, and from string-theoretic point of view, stability conditions on smooth projective threefolds are the most interesting ones. In this talk, I will recall some important notions associated to derived categories of varieties and stability conditions, with special emphasis on curves and surfaces.
Sala 2
2017-03-06
12:00hrs.
Seminario de Estadística
Garritt Page. Brigham Young University
Estimation and Prediction in the Presence of Spatial Confounding for Spatial Linear Models
Abstract:

In studies that produce data with spatial structure it is common that covariates of interest vary spatially in addition to the error. Because of this,  the error and covariate are often correlated. When this occurs it is difficult to distinguish the covariate effect from residual spatial variation.  In an iid normal error setting, it is well known that this type of correlation produces biased coefficient estimates but predictions remain unbiased.  In a spatial setting  recent studies have shown that coefficient estimates remain biased, but spatial prediction has not been addressed. The purpose of this paper is to provide a more detailed study of coefficient estimation from spatial models when covariate and error are correlated and then begin a formal study regarding spatial prediction. This is carried out by investigating properties of the generalized least squares estimator and the best linear unbiased predictor when a spatial random effect and a covariate are jointly modeled. Under this setup we demonstrate that the mean squared prediction error is possibly reduced when covariate and error are correlated.  


Sala 2, Facultad de Matemáticas
2017-01-16
17:00hrs.
Seminario de Sistemas Dinámicos
Luna Lomonaco. Usp
The Mandelbrot set and its satellite copies
Abstract:
For a polynomial on the Riemann sphere, infinity is a (super) attracting fixed point, and the filled Julia set is the set of points with bounded orbit. Consider the quadratic family $P_c(z)=z^2+c$. The Mandelbrot set M  is the set of parameters c such that the filled Julia set of $P_c$ is connected. Douady and Hubbard, using renormalization, proved the existence of homeomorphic copies of M inside of M, which can be primitive (if, roughly speaking, they have a cusp) or satellite (if they don't). They conjectured that the primitive copies of M are quasiconformal homeomorphic to M, and that the satellite ones are quasiconformal homeomorphic to M outside any small neighbourhood of the root. These results are now theorems due to Lyubich. The satellite copies are not quasiconformal homeomorphic to M, but are they mutually quasiconformally homeomorphic? In a joint work with C. Petersen we prove that this question, which has been open for about 20 years, has in general a negative answer.
Sala 1, Fac. Mates, PUC
2017-01-16
16:00hrs.
Seminario de Sistemas Dinámicos
Jiangang Yang. Uff
Continuity of Lyapunov exponents in the C0 topology
Abstract:
This is a joint with Marcelo Viana.
We prove that the Bochi-Mañé theorem is false, in general, for linear cocycles over non-invertible maps: there are $C_0$-open subsets of linear cocycles that are not uniformly hyperbolic and yet have Lyapunov exponents bounded from zero.
Sala 1, Fac. Mates, PUC
2017-01-13
14:40 Hrshrs.
Seminarios Extraordinarios
Tyrone Crisp . Max- Planck Institute For Mathematics, Bonn
Representation theory of reductive groups via operator algebras and their modules
Abstract:

Abstract: Operator algebra theory combines algebra and functional analysis to study collections of linear operators. Applications to the study of infinite-dimensional group representations have been a major driving force in the development of operator algebra theory from the 1940s up to the present. In this talk I shall present a novel approach to the representation theory of real reductive groups (for example, GL(n,R)) using operator-algebraic techniques. (This is partly based on joint work with P. Clare, N. Higson and R. Yuncken.)


Sala 2 Facultad de Matemáticas
2017-01-13
16hrs.
Coloquio de Matemática UC
Javier Arsuaga. Department Of Mathematics & Department Of Molecular And Cellular Biology, UC Davis
Using random knot theory to understand the three dimensional organization of genomes
Abstract:

Uncovering the basic principles that govern the three dimensional (3D) organization of genomes poses one of the main challenges in mathematical biology of the postgenomic era. Certain viruses and some organisms, such as trypanosomes, accommodate knotted or linked genomes. Others, such as bacteria, are known to have unknotted genomes. It remains to be determined if the genomes of higher organisms, such as humans, admit topologically complex forms. 

 

In this talk I will present some mathematical results and computational methods that have been developed when addressing these biological questions. Biological implications of these results will also be discussed.


Sala 2
2017-01-12
16:00 hrs hrs.
Seminarios Extraordinarios
Benjamin Matschke. Max Planck Institute For Mathematics, Bonn
Discrete versus continuous - topics in discrete geometry, topology and number theory.
Abstract:
In many fields of mathematics there is an interplay between
the discrete and the continuous world, sometimes through analogies
between statements, and sometimes methods from one side need to be
used to solve problems on the other side, and vice versa.
This talk is essentially on some interesting examples of that:
Geometric incidence theorems, colored Tverberg theorems*, successive
spectral sequences, and S-unit equations**.

* Joint with Pavle Blagojevi?, Günter Ziegler, and Roman Karasev.
** Joint with Rafael von Känel.
Sala 2
2017-01-11
15:00hrs.
Seminario de Análisis y Geometría
Marie-Françoise Bidaut-Véron. Université François Rabelais, Tours, France
A priori estimates and ground states of solutions of an Emden-Fowler equation with gradient
Sala 2, Facultad de Matemáticas UC
2017-01-11
16:00hrs.
Seminario de Análisis y Geometría
Laurent Véron. Université François Rabelais, Tours, France
Initial trace of positive solutions of some nonlinear diffusion equations
Sala 2, Facultad de Matemáticas UC
2017-01-11
12:00hrs.
Seminario de Estadística
Marc G. Genton. King Abdullah University Of Science And Technology (Kaust), Saudi Arabia
Computational Challenges with Big Environmental Data
Abstract:

Two types of computational challenges arising from big environmental data

are discussed. The first type occurs with multivariate or spatial

extremes. Indeed, inference for max-stable processes observed at a large

collection of locations is among the most challenging problems in

computational statistics, and current approaches typically rely on less

expensive composite likelihoods constructed from small subsets of data. We

explore the limits of modern state-of-the-art computational facilities to

perform full likelihood inference and to efficiently evaluate high-order

composite likelihoods. With extensive simulations, we assess the loss of

information of composite likelihood estimators with respect to a full

likelihood approach for some widely-used multivariate or spatial extreme

models. The second type of challenges occurs with the emulation of climate

model outputs. We consider fitting a statistical model to over 1 billion

global 3D spatio-temporal temperature data using a distributed computing

approach. The statistical model exploits the gridded geometry of the data

and parallelization across processors. It is therefore computationally

convenient and allows to fit a non-trivial model to a data set with a

covariance matrix comprising of 10^{18} entries. We provide 3D

visualization of the results. The talk is based on joint work with Stefano

Castruccio and Raphael Huser.

 


Sala 2, Facultad de Matemáticas
2017-01-11
11:00hrs.
Seminario de Estadística
Ying Sun. King Abdullah University Of Science And Technology (Kaust), Saudi Arabia
Total Variation Depth for Functional Data
Abstract:

There has been extensive work on data depth-based methods for robust

multivariate data analysis. Recent developments have moved to

infinite-dimensional objects such as functional data. In this work, we

propose a new notion of depth, the total variation depth, for functional

data. As a measure of depth, its properties are studied theoretically, and

the associated outlier detection performance is investigated through

simulations. Compared to magnitude outliers, shape outliers are often

masked among the rest of samples and harder to identify. We show that the

proposed total variation depth has many desirable features and is well

suited for outlier detection. In particular, we propose to decompose the

total variation depth into two components that are associated with shape

and magnitude outlyingness, respectively. This decomposition allows us to

develop an effective procedure for outlier detection and useful

visualization tools, while naturally accounting for the correlation in

functional data. Finally, the proposed methodology is demonstrated using

real datasets of curves, images, and video frames. The talk is based on

joint work with Huang Huang.


Sala 2, Facultad de Matemáticas
2017-01-09
15:00 Hrs.hrs.
Seminarios Extraordinarios
Mircea Petrache. Max- Planck Institute For Mathematics, Bonn
Sharp asymptotics and equidistribution for large particle systems with long-range interactions
Abstract:
We consider the asymptotic behaviour of systems of a very large number of particles subject to long-range pairwise repulsive interactions.  Such questions appear in several branches of mathematics, such as the study of Fekete points in constructive approximation, Ginzburg-Landau vortex models for superconductors, or in the study of random matrices.  Jointly with Sylvia Serfaty we obtained the characterization of the behavior of the system at the microscopic scale: When the temperature tends to zero, our gas "crystallizes" to a minimizer of W, conjectured to be the "Abrikosov" triangular lattice in 2 dimensions.
Steps towards such strong structural results are equidistribution results obtained in joint works with Simona Rota-Nodari and the development of tools for studying minimisation problems on lattices, with Laurent Betermin. 
I will also mention the link to the asymptotics for multimarginal optimal transport problems appearing in computational chemistry, as well as other future directions of investigation.

Sala 1 de la Facultad de Matemáticas de la P. Universidad Católica de Chile
2017-01-09
16:30 Hrs.hrs.
Seminario Local de Sistemas Dinámicos
Ian Morris, Surrey.
Matrix thermodinamic formalism
Abstract:

 

Equilibrium states of real-valued potentials over subshifts of finite type have been investigated since the 1970s and their basic ergodic properties have long been well understood: they are exponentially mixing, Bernoulli and have positive entropy. Much more recently a theory has emerged of equilibrium states associated to matrix-valued potentials. In this talk I will describe how the ergodic properties of a matrix equilibrium state depend on the semigroup generated by the underlying matrices. At the end I will discuss some consequences for self-affine fractals in the plane.

 

Sala 1 de la Facultad de Matemáticas de la Universidad Católica
2017-01-06
16:00hrs.
Coloquio de Matemática UC
Valery Alexeev. University Of Georgia
Volumes of open surfaces
Abstract:
The volume of a smooth projective variety measures asymptotically the number of pluricanonical sections. For a surface, it is a positive integer. Similarly, the volume of an open smooth surface measures the number of pluri LOG canonical sections. Easy examples show that it could be a rational number. If nonzero, how small could it be? I will discuss some general results in this area and the new records obtained jointly with Wenfei Liu.
Sala 2
2017-01-05
17:00hrs.
Seminario de Teoría Espectral
Jake Fillman. Virginia Tech
Ballistic propagation for limit-periodic Jacobi operators
Abstract:
We will talk about the propagation of wave packets in a one-dimensional medium with limit-periodic background potential. If the amplitudes of the low-frequency modes of the potential decay sufficiently rapidly, then wavepackets travel ballistically in the sense that the group velocity is injective on the domain of the position operator. Since the underlying Hamiltonian has purely absolutely continuous spectrum, this answers a special case of a general question of J. Lebowitz regarding the relationship between ac spectrum and ballistic wavepacket spreading.
Sala 1
2017-01-03
16:00 hrs.hrs.
Seminarios Extraordinarios
Giancarlo Lucchini. Centre de Mathématiques Laurent Schwartz
Congruencias, aproximación y grupos algebraicos
Abstract:
Cuando uno estudia las soluciones racionales de ecuaciones polinomiales, una pregunta que uno puede hacerse es si éstas son densas en el conjunto de las soluciones reales.  De forma análoga.  Uno puede hacerse la misma pregunta para otras completaciones de Q, es decir para lo que uno llama los números p-ádicos.  Sin embargo, esta segunda pregunta puede ser traducida en términos de simples congruencias módulo n para un cierto entero n.  El objetivo de esta charla es estudiar ambas preguntas simultáneamente para un conjunto particular de ecuaciones: aquellas cuyo conjunto de soluciones posee una estructura de grupo. En términos más técnicos, estudiaremos la propiedad de "aproximación débil" para los "grupos algebraicos".  Mirando un ejemplo muy particular (la ecuación x^2 + y^2 = 1), veremos cómo la estructura de grupo puede ser usada para probar (o refutar) esta propiedad en el caso de los grupos algebraicos lineales, como fue hecho por Sansuc en 1981.
Sala 2 de la Facultad de Matemáticas