Seminarios

Futuros Eventos

2024-04-23
13:30hrs.
Seminario de Geometría Algebraica
Francisco Gallardo. UC Chile
Annihilating The Cohomology of Group Schemes
sala 2
2024-04-16
13:30hrs.
Seminario de Geometría Algebraica
Felipe Hernández. UC Chile
On Coverings of Deligne-Mumford Stacks and Surjectivity of The Brauer Map
sala 2
2024-04-11
10:00hrs.
Seminario Cuerpos de Clase Explícitos
Rodrigo Galaz. UC
Cuerpo de Clases de Hilbert y Morfismo de Artin II
Sala multiusos 1 (primer piso Villanueva)
2024-04-10
17:20-18:50 (30min presentacion + 1h discusion)hrs.
Club de Lectura y Discusion "matematica X Deep Learning"
Nicolas Alvarado. UC Chile
Entrenamiento de Redes Neuronales Hiperbolicas -- Https://arxiv.org/pdf/2104.10727.pdf
Sala 1
2024-04-09
16:10hrs.
Seminario de Lógica Matemática
Benjamín Oyarzún. Rwth Aachen Universität
No-Decibilidad del Cálculo de Secuentes
Sala Multiusos
Abstract:
En este seminario se pretende demostrar la inexistencia de un programa capaz de decidir la satisfacibilidad de una fórmula sin variables libres en la lógica de primer orden, es decir, no existe un programa que pueda demostrar o refutar conjeturas matemáticas arbitrarias en el contexto de FO.
2024-04-09
13:30hrs.
Seminario de Geometría Algebraica
Marcos Canedo. UC Chile
La Conjetura Qhd y el Intento de Demostración
sala 2
2024-04-05
14:30hrs.
Seminario Pre Santas
Riccardo Pengo. Leibniz Universität Hannover
Mahler Measures, From Small Heights To Big Conjectures 2
Sala 2 de usos múltiples del primer piso del edificio Felipe Villanueva
2024-04-05
16:10hrs.
Coloquio de Matemática UC
Rodolfo Gutiérrez-Romo. Universidad de Chile
...
Auditorio Ninoslav Bralic
2024-04-04
16:00hrs.
Seminario Fismat
-. -
Grupo de Estudio
Sala 1 - Facultad de Matemáticas
2024-04-04
10:00hrs.
Seminario Cuerpos de Clase Explícitos
Rocío Sepúlveda. UC
Cuerpo de Clases de Hilbert y Morfismo de Artin I
Sala multiusos 1 (primer piso Villanueva)
2024-04-04
16:10hrs.
Seminario de Lógica Matemática
Renato Lewin. PUC
Algebrización de la Lógica
Sala Multiusos
Abstract:
En esta charla desarrollaremas las herramientas para generalizar el proceso de Lindenbaum-Tarski estudiado la vez anterior a otros sistemas lógicos clásicos y no clásicos
2024-04-03
14:30hrs.
Seminario Pre Santas
Riccardo Pengo. Leibniz Universität Hannover
Mahler Measures, From Small Heights To Big Conjectures 1
Sala 2 de usos múltiples del primer piso del edificio Felipe Villanueva
2024-04-03
17:00-18:30 (30min presentacion, 1h discusion)hrs.
Club de Lectura y Discusion "matematica X Deep Learning"
Felipe Urrutia. Universidad de Chile
Uso de Teoria de Informacion en Procesamiento de Lenguaje Natural -- Https://proceedings.neurips.cc/paper_Files/paper/2023/hash/08Eac13583B310Ec55D755F99C549Be3-Abstract-Conference.html
Sala 1
2024-04-03
13:40hrs.
Seminario de Ingeniería Matemática y Computacional
Marcos Goycoolea. Escuela de Administración UC
Precedence Constrained Linear Optimization and Applications in Scheduling & Mining
Presencial en Auditorio Edificio San Agustín
Abstract:
We examine a class of mixed integer linear programming problems characterized by having a large set of precedence constraints and a small number of additional, “arbitrary” side constraints. These problems, which in a way are “almost” totally unimodular, are applicable in a wide array of scheduling tasks, including the well-known Resource-Constrained Project Scheduling Problem (RCPSP). RCPSPs and their variants are known to be extremely difficult to solve in practice. Moreover, they are of particular importance in the field of mining, where the scale of the problems can involve hundreds of millions of variables, posing a challenge for standard commercial solvers.
 
In this talk will describe these precedence-constrained optimization problems and discuss how understanding the optimal solution structure can inform the creation of specialized linear programming techniques that are more scalable than traditional algorithms. We will also describe new classes of cutting planes to strengthen linear relaxations. Applications of these methods will be showcased, ranging from scheduling for open pit and underground mines to adapting to uncertainties and integrating environmental objectives into scheduling practices.
 
This is joint work with Patricio Lamas, Eduardo Moreno and Orlando Rivera.
2024-04-02
13:30hrs.
Seminario de Geometría Algebraica
Juan Pablo Zúñiga. UC Chile
Otra Conjetura Con los Números de Markov y el Plano
sala 2
2024-04-02
16:10hrs.
Seminario de Estudiantes de Doctorado en Estadística
Daniel Saavedra. PUC
Generate Censored Samples: Controlling The Desired Censorship Percentage
SALA 3, FACULTAD DE MATEMÁTICAS
Abstract:

Generating censored random samples while controlling the desired percentage of censorship is a critical task when assessing the performance of our model in corresponding simulation studies. In this presentation, we will explore an approach to aboard this challenge, particularly when dealing with random censorship. This method is implemented in the recently available 'rcens' package on CRAN, which also offers functionalities to control the censorship percentage in generated samples with different types of censorship (Types I, II, and III), providing researchers and professionals with a straightforward tool to simulate datasets according to desired distributional needs. Lastly, we will discuss a potential scheme for generating interval censorship also implemented in 'rcens'.

2024-04-01
16:30hrs.
Seminario de Sistemas Dinámicos
Erwan Lanneau. Université Grenoble Alpes / Institut Fourier
Minimum Expansion Factors of Orientation-Reversing Pseudo-Anosov Maps
Sala de Seminarios (7° piso), Facultad de Ciencias Físicas y Matemáticas (Edificio Beauchef 851), Universidad de Chile
Abstract:
Pseudo-Anosov maps are prevalent among mapping classes of surfaces. Given a pA map, the expansion factor measures the complexity of its dynamics. It is a classical result that the set of expansion factors (viewed as a subset of the set of real numbers) among all pA maps defined on a fixed surface has a minimum element. This minimum expansion factor can be thought of as the systole of the moduli space for the Teichmüller metric. Its value is not known for the genus larger than three.

In this talk, we will present some recent progress on the asymptotic of this minimum (normalized) expansion factor for orientation reversing Pseudo-Anosov maps. The talk will be elementary.

This is a recent joint work with Livio Liechti and Chi Cheuk Tsang.

Eventos Pasados

2024-03-28
10:00hrs.
Seminario Cuerpos de Clase Explícitos
Benjamín Macías. UC
Ramificación
Apoquindo 4499, cowork 2
2024-03-27
13:40hrs.
Seminario de Ingeniería Matemática y Computacional
Vamsi Potluru. Ai Research, Jp Morgan
Synthetic data in Finance
Abstract:
I will give a broad introduction to synthetic data and in particular their applications to Finance. I will focus on fair synthetic data based on creating a small coreset of the original dataset utilizing the Wasserstein distance while enforcing demographic parity. Experiments show the benefits of the approach and will also include reducing bias in LLMs. The talk will be broadly based on:
 
https://arxiv.org/abs/2401.00081
 
https://arxiv.org/abs/2311.05436

Presencial en Auditorio Edificio San Agustín
2024-03-26
13:30hrs.
Seminario de Geometría Algebraica
Vicente Monreal. UC Chile
Clasificación superficies con K^2=2p_g-3
sala 2
2024-03-25
11:00hrs.
Seminario de Probabilidades y Geometría en Grupos
Vicente Urria. UC
Cadenas de Markov y Random Walks
Sala 2
2024-03-25
13:40hrs.
Seminario de Ingeniería Matemática y Computacional
Rashmi Vinayak. School of Computer Science, Carnegie Mellon University
Unlocking the Code: How Math Protects Our Data at Scale
Abstract:
The massive data centers storing our information face constant challenges: hardware failures, unpredictable performance, and limited resources. How can we ensure our data stays safe and accessible in this ever-changing environment? This talk explores the surprising power of coding theory, a branch of mathematics that helps us store data efficiently and safely even when systems malfunction. I will start by delving into the basic principles behind coding theory and showing how it is used in modern storage systems. Finally, I will present a peek into cutting-edge research that's pushing the boundaries of data protection with even smarter codes.
Sala multiusos, primer piso Edificio Felipe Villanueva.
2024-03-21
16:10hrs.
Seminario de Lógica Matemática
Renato Lewin. PUC
Algebrización de la Lógica
Abstract:
Las oraciones de la lógica proposicional clásica verifican una serie de propiedades algebraicas simlilares a las de los números. Esto sugiere hacer un tratamiento algebraico de la lógica. Adelantándose a su tiempo George Boole sentó las bases de este estudio. Ya en el siglo XX, Alfred Tarski hizo la construcción general que asocia este cálculo proposicional con una clase de álgebras que se denominan álgebras de Boole.

En esta charla estudiaremos con cierto detalle esta relación.
Sala 2, Edificio Rolando Chuaqui
2024-03-21
16:10hrs.
Seminario de Análisis y Geometría
Jean Dolbeault. Ceremade, Université Paris-Dauphine
Nonlinear diffusions, entropies and stability in functional inequalities
Abstract:
Entropy methods coupled to nonlinear diffusions are powerful tools to study some functional inequalities of Sobolev type. Self-similar solutions can indeed be reinterpreted as optimal solutions of Aubin-Talenti type. A notion of generalized entropy is the key tool which relates the nonlinear regime to the linearized problem around the asymptotic profile and reduces the analysis to a spectral problem. Estimates can be made constructive. This gives quantitative stability results with explicit constants. Entropy methods will be compared with other direct methods, intended for instance to obtain bounds on the stability constant in the Bianchi-Egnell stability result for the Sobolev inequality.

Sala 5
2024-03-21
16:00hrs.
Seminario Fismat
Jakub Czartowski. Jagiellonian University, Krakow, Poland
Trade-off relations for operation entropy of complementary quantum channels
Abstract:
Completely Positive Trace Preserving (CPTP) maps are connected to the notion of quantum channels, which provide the largest possible set of allowed operations in the theory of quantum open systems. Every such map is connected via a canonical Naimark extension to a unitary operation on a bipartite system and, in turn, to a complementary map defined as its action to the second, auxiliary, subsystem. IN this talk we will discuss a notion of map entropy connected to the CPTP maps and their complementary counterparts, the relation between the two quantities and demonstrate the bounds that need to be satisfied by these quantities. The talk will conclude with several related open problems.
 

Sala 1 - Facultad de Matemáticas
2024-03-20
17:00 - 18:00hrs.
Club de Lectura y Discusion "matematica X Deep Learning"
Mircea Petrache. UC Chile
Repaso inicial: Redes neuronales, entrenamiento, arquitecturas basicas (CNN, GNN, RNN, Transformers, Difusion)
Abstract:
Se recuerdan / introducen las redes neuronales y sus arquitecturas.

Sesion util especialmente para quienes no han visto redes neuronales antes.

La presentacion sera muy rapida y no sustituye un estudio individual, aca van mas materiales introductorios.

Material:

Notas que cubren entrenamiento, CNN y RNN https://arxiv.org/pdf/2304.05133.pdf

Notas un poco mas avanzadas/matematicas, sin enfasis en arquitecturas especiales: https://arxiv.org/abs/2105.04026

Notas sobre GNN (graph neural networks): http://web.stanford.edu/class/cs224w/slides/04-GNN2.pdf

Transformers (intro visual): https://jalammar.github.io/illustrated-transformer/

Difusion (paper de introduccion/survey): https://arxiv.org/pdf/2306.04542.pdf


Sala 1
2024-03-19
13:30hrs.
Seminario de Geometría Algebraica
Jaime Negrete. UC Chile
Automorfismos de singularidades
sala 2
2024-03-18
11:00hrs.
Seminario de Probabilidades y Geometría en Grupos
Miguel Donoso. UC
Preliminares geométricos y probabilísticos
Sala 2
2024-03-18
16:30hrs.
Seminario de Sistemas Dinámicos
Pablo Amster. Universidad de Buenos Aires
Una versión abstracta de la desigualdad de Gronwall
Abstract:
¿Es posible considerar el lema de Gronwall como un principio del máximo? En esta charla elemental presentaremos una versión abstracta del lema, en términos de la cota espectral de un operador definido en un látice de Banach. Como consecuencia, deduciremos versiones generalizadas del lema, así como aplicaciones a sistemas discretos y resultados de unicidad para problemas semilineales.
Sala de Seminarios Maryam Mirzakhani, Departamento de Matemáticas, Campus Juan Gómez Millas, Universidad de Chile
2024-03-14
16:10hrs.
Club de Matemática
Santiago Saglietti. UC
Al barajar cartas, ¿7 es número ganador?. 
Abstract:
¿Cuántas veces es necesario barajar un mazo de cartas para que esté bien mezclado? En un artículo del New York Times de 1990, titulado ”Al barajar cartas, el 7 es número ganador”, su autor Kolata escribe ”los matemáticos Bayer y Diaconis han demostrado que sólo hace falta barajar siete veces un mazo, de manera ordinaria, para que esté bien mezclado. Menos de siete no es suficiente y hacerlo ms de siete no produce mejoras significativas”. En esta charla vamos a intentar explicar de manera elemental la matemática detrás de barajar un mazo de cartas, qué fue exactamente lo que probaron Bayer y Diaconis y que hay de cierto en las palabras de Kolata.
Facultad de matemáticas, sala multiusoshttp://clubdematematica.mat.uc.cl/
2024-03-14
17:30-18:30hrs.
Club de Lectura y Discusion "matematica X Deep Learning"
Mircea Petrache. UC Chile
Fijamos formato y proponemos temas por abordar durante el semestre
Abstract:
Consideraremos tematicas que mezclen herramientas matematicas con aplicaciones/ideas de aprendizaje profundo.

Una primera idea es que
-- cada sesion tenga 30 min de presentacion de un paper o tema,
-- y sucesivamente prevedemos max 1 hora de discusiones, donde incluso se cubre material complementario y se discuten los detalles del paper.
-- Para cada sesion sirve que al menos 2-3 personas hayan leido el paper y que lo conozcan.

En esta primera ocasion, hablaremos de lo siguiente:
-- si lo de arriba es un buen formato,
-- que temas interesa cubrir (sobre que temas buscamos papers por presentar)
-- ademas nos presentamos entre los interesados en matematicas + deep learning
Sala 2
2024-03-11
11:00hrs.
Seminario de Probabilidades y Geometría en Grupos
Vicente Urria. UC
Geometría en grafos de Cayley
Sala 2
2024-01-22
11:00hrs.
Seminario de Sistemas Dinámicos
Adrián Esparza. Universidad Austral de Chile
Dominios de Baker hiperbólicos y formalismo termodinámico
Abstract:
Aplicamos técnicas de formalismo termodinámico a una familia de funciones enteras que tiene dominios de Baker de tipo hiperbólico probando la existencia de medidas conformes y obteniendo una fórmula de tipo Bowen para la dimensión de Hausdorff de un subconjunto “dinámicamente bueno” del conjunto de Julia. (Este es un trabajo conjunto con I. Inoquio)
Sala 2
2024-01-22
16:00hrs.
Coloquio de Matemática UC
Gunther Uhlmann. University of Washington
Travel Time tomography and boundary rigidity
Abstract:
We will consider the inverse problem of determining the sound speed or
index of refraction of a medium by measuring the travel times of waves
going through the medium. This problem arises in global seismology in
an attempt to determine the inner structure of the Earth by measuring
travel times of earthquakes. It also has several applications in
optics and medical imaging among others.

The problem can be recast as a geometric one:  Can one determine
the Riemannian metric of a Riemannian manifold with boundary by
measuring the distance function between boundary points? This is the
boundary rigidity problem. We will also consider the problem of
determining the metric from the scattering relation, the so-called
lens rigidity problem. No previous knowledge of differential
geometry will be assumed.
 

Edificio Villanueva
2024-01-18
14:30hrs.
Coloquio de Estadística y Ciencia de Datos de la Pontificia Universidad Católica de Chile
Manuel González. Universidad de la Frontera
Métodos de regularización aplicados a problemas de quimiometría
Sala 2
2024-01-18
11:30hrs.
Coloquio de Estadística y Ciencia de Datos de la Pontificia Universidad Católica de Chile
Christian Caamaño . Universidad del Bio-Bio
A flexible Clayton-like spatial copula with application to bounded support data.
Abstract:
The Gaussian copula is a powerful tool that has been widely used to model spatial and/or temporal correlated data with arbitrary marginal distribution. However, this kind of model can potentially be too restrictive since it expresses a reflection symmetric dependence. In this work, we propose a new spatial copula model that allows to obtain random fields with arbitrary marginal distribution with a type of dependence that can be reflection symmetric or not.
Particularly, we propose a new random field with uniform marginal distribution, that can be viewed as a spatial generalization of the classical Clayton copula model. It is obtained through a power transformation of a specific instance of a beta random field which in turn is obtained using a transformation of two independent Gamma random fields.
For the proposed random field we study the second-order properties and we provide analytic expressions for the bivariate distribution and its correlation. Finally, in the reflection symmetric case, we study the associated geometrical properties.
As an application of the proposed model we focus on spatial modeling of data with bounded support. Specifically, we focus on spatial regression models with marginal distribution of the beta type. In a simulation study, we investigate the use of the weighted pairwise composite likelihood method for the estimation of this model. Finally, the effectiveness of our methodology is illustrated by analyzing point-referenced vegetation index data using the Gaussian copula as benchmark. Our developments have been implemented in an open-source package for the R statistical environment.

Keywords: Archimedean Copula, Beta random fields, Composite likelihood, Reflection Asymmetry.
Sala 2
2024-01-18
15:30hrs.
Coloquio de Estadística y Ciencia de Datos de la Pontificia Universidad Católica de Chile
Daira Velandia. Universidad de Valparaíso
Estimation methods for a Gaussian process under fixed domain asymptotics
Abstract:
This talk will address some inference tools for Gaussian random fields from the increasing domain and fixed domain asymptotic approaches. First, concepts and previous results are presented. Then, the results obtained after studying some extensions of the problem of estimating covariance parameters under the two asymptotic approaches named above are addressed.
Sala 2
2024-01-15
16:30hrs.
Seminario de Sistemas Dinámicos
Borys Kuca. Jagiellonian University
Multiple ergodic averages along polynomials for systems of commuting transformations
Abstract:
The last 50 years have seen tremendous activity at the interface between ergodic theory, combinatorics and number theory that started with Furstenberg’s dynamical proof of the Szemerédi theorem from the 1970s. The goal of this line of research has been to prove new multiple recurrence results and then deduce combinatorial corollaries. To achieve this, one wants to understand the limiting behaviour of relevant multiple ergodic averages. Of particular interest are averages of commuting transformations with polynomial iterates: they play a central role in the polynomial Szemerédi theorem of Bergelson and Leibman. While their norm convergence has been established in a celebrated paper of Walsh, little more has been known for a long time about the form of the limit. In this talk, I will present some recent results on the limits of such averages obtained jointly with Nikos Frantzikinakis and explain how they can be used to answer a number of previously intractable problems at the intersection between ergodic theory and combinatorics.
Sala de Seminarios 7° Piso, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
2024-01-12
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Brendan Keith. Division of Applied Mathematics, Brown University
Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints
Abstract:
The proximal Galerkin finite element method is a high-order, nonlinear numerical method that preserves the geometric and algebraic structure of bound constraints in infinite-dimensional function spaces. In this talk, we will introduce the proximal Galerkin method and apply it to solve free-boundary problems, enforce discrete maximum principles, and develop scalable, mesh-independent algorithms for optimal design. The proximal Galerkin framework is a natural consequence of the latent variable proximal point (LVPP) methodology, which is a stable and robust alternative to the interior point method that will also be introduced in this talk. LVPP can be viewed as a low-iteration complexity, infinite-dimensional optimization algorithm that may be viewed as having an adaptive barrier function that is updated with a new informative prior at each (outer loop) optimization iteration. One of the main benefits of this algorithm is witnessed when analyzing the classical obstacle problem. Therein, we find that the original variational inequality can be replaced by a sequence of semilinear partial differential equations (PDEs) that are readily discretized and solved with, e.g., high-order finite elements. Throughout the talk, we will arrive at several unexpected contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and an infinite-dimensional Lie group; and (3) a gradient-based, bound-preserving algorithm for two-field density-based topology optimization. The complete latent variable proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. This is joint work with T.M. Surowiec.

Presencial en Auditorio Edificio San Agustín
2024-01-10
13:30hrs.
Seminario de Ingeniería Matemática y Computacional
Dr. Guido Kanschat. Decano de la Facultad de Ingeniería; Centro Interdisciplinario de Computación Científica (Iwr); Universidad de Heidelberg
Constructing Multigrid Solvers for Hybridized Finite Elements
Abstract:
We begin by reviewing the derivation and motivation of hybridized mixed finite element methods and hybridized discontinuous Galerkin (HDG) methods. In the second part of the talk, we discuss the benefits and inner workings of multigrid solvers. Then, we are ready to discuss multigrid solvers for HDG methods, where the focus is on the construction of intergrid operators. In particular, we show how the analysis of existing methods leads to the development of new schemes.
Presencial en Auditorio Edificio San Agustín
2024-01-10
11:10hrs.
Facultad
Pedro Gaspar. PUC
Topolodías en Santiago https://sites.google.com/view/topolodias-stgo/programa
Sala Multiuso 1° piso /1https://sites.google.com/view/topolodias-stgo/programa
2024-01-10
14:50 - 16:00hrs.
Seminario de Geometría Algebraica
Jonny Evans. University of Lancaster
Mini-curso en Topolodías en Santiago: Singularidades y topología II
Sala Multiuso 1° piso /1https://sites.google.com/view/topolodias-stgo/home
2024-01-09
12:20 - 13:30hrs.
Seminario de Geometría Algebraica
Angelica Simonetti. University of Lancaster
Sesión especial en Topolodías en Santiago: geometría algebraica y topología
Sala Multiuso 1° piso /1https://sites.google.com/view/topolodias-stgo/home
2024-01-09
14:50 - 16:00hrs.
Seminario de Geometría Algebraica
Jonny Evans. University of Lancaster
Mini-curso en Topolodías en Santiago: Singularidades y topología I
Sala Multiuso 1° piso /1https://sites.google.com/view/topolodias-stgo/home
2024-01-09
11:10hrs.
Facultad
Mauricio Bustamante - . PUC
Topolodías en Santiago
Abstract:
Tendremos charlas en las que se presentarán algunos de los prerrequisitos para seguir el minicurso que imparte Jonny Evans. Luego continuaremos con el minicurso en sí y ponencias sobre temas relacionados.
 
 
Todas las charlas serán en la sala de usos múltiples 1. Primer piso del edificio Felipe Villanueva.

Sala Multiuso 1° piso /1https://sites.google.com/view/topolodias-stgo/home
2024-01-08
12:20hrs.
Facultad
Mauricio Bustamante. PUC
Topolodías en Santiago https://sites.google.com/view/topolodias-stgo/programa
Abstract:
Tendremos charlas en las que se presentarán algunos de los prerrequisitos para seguir el minicurso que imparte Jonny Evans. Luego continuaremos con el minicurso en sí y ponencias sobre temas relacionados.

https://sites.google.com/view/topolodias-stgo/programa
sala de usos múltiples 1. Primer piso del edificio Felipe Villanueva.https://sites.google.com/view/topolodias-stgo/programa
2024-01-08
11:00 hrs hrs.
Facultad
Felipe Riquelme . Pontificia Universidad Católica de Valparaíso (Pucv)
Medidas invariantes para el flujo horocíclico
Abstract:
Abstract: El objetivo principal de este mini curso es estudiar el conjunto de medidas invariantes por el flujo horocíclico en superficies hiperbólicas. En el caso de una superficie compacta Furstenberg probó que el flujo horocíclico es únicamente ergódico, siendo la medida de Liouville la única medida de probabilidad invariante. En el caso de una superficie de volumen finito Dani probó que toda medida de probabilidad invariante es, o bien la medida de Liouville, o bien una medida soportada en una órbita periódica. En el caso de una superficie geométricamente finita Roblin probó que existe una única medida soportada en todo el conjunto no errante, medida que es infinita. Finalmente, un trabajo reciente de Landesberg y Lindenstrauss clasifican a las medidas invariantes infinitas en el caso de cubrimientos regulares de superficies geométricamente finitas. En este curso se espera probar los resultados de Furstenberg, Dani y Roblin en 3 sesiones. El gran interés de este curso es evidenciar las obstrucciones geométricas que determinan las
distintas clasificaciones en cada caso y dar cuenta de las consecuencias en equidistribución de órbitas periódicas horocíclicas.
Sala 1, Edificio Rolando Chuaqui
2024-01-08
16:30hrs.
Seminario de Sistemas Dinámicos
Neil Mañibo. Universität Bielefeld
Uniquely ergodic subshifts over compactifications of the naturals
Abstract:
In this talk, we will discuss one-dimensional substitution subshifts over (infinite) compact alphabets and their dynamical properties. As a motivating class, we will focus on shifts generated by a parametrised family of substitutions on certain compactifications of the natural numbers. We will provide a general checkable condition for unique ergodicity that relies on compactness properties of the substitution operator, which the analogue of the substitution matrix for infinite alphabets. This is based on joint work with Dan Rust and Jamie Walton, and Dirk Frettloeh and Alexey Garber.
Sala de Seminarios 7° Piso, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
2024-01-04
16:10hrs.
Seminario de Análisis y Geometría
Cristian González Riquelme. Instituto Superior Tecnico, Lisbon
How regular is the maximal function of a given function?
Abstract:
Maximal operators are a central object in harmonic analysis. The regularity theory of such objects has been an object of study formany authors over the last decades. However, even in the one dimensional case, there are still interesting questions that remain open. In this talk, we will discuss recent developments and open questions about this topic, particularly about the boundedness and continuity for such operators at the derivative level and regularity improving properties of these operators.
Sala Multiuso 1° piso, edificio Felipe Villanueva
2024-01-04
11:00 hrshrs.
Facultad
Felipe Riquelme. Pontificia Universidad Católica de Valparaíso (Pucv)
Medidas invariantes para el flujo horocíclico
Abstract:
Abstract: El objetivo principal de este mini curso es estudiar el conjunto de medidas invariantes por el flujo horocíclico en superficies hiperbólicas. En el caso de una superficie compacta Furstenberg probó que el flujo horocíclico es únicamente ergódico, siendo la medida de Liouville la única medida de probabilidad invariante. En el caso de una superficie de volumen finito Dani probó que toda medida de probabilidad invariante es, o bien la medida de Liouville, o bien una medida soportada en una órbita periódica. En el caso de una superficie geométricamente finita Roblin probó que existe una única medida soportada en todo el conjunto no errante, medida que es infinita. Finalmente, un trabajo reciente de Landesberg y Lindenstrauss clasifican a las medidas invariantes infinitas en el caso de cubrimientos regulares de superficies geométricamente finitas. En este curso se espera probar los resultados de Furstenberg, Dani y Roblin en 3 sesiones. El gran interés de este curso es evidenciar las obstrucciones geométricas que determinan las
distintas clasificaciones en cada caso y dar cuenta de las consecuencias en equidistribución de órbitas periódicas horocíclicas.
Sala 1, Edificio Rolando Chuaqui
2024-01-03
11:00 hrs hrs.
Facultad
Felipe Riquelme . Pontificia Universidad Católica de Valparaíso (Pucv)
Medidas invariantes para el flujo horocíclico
Abstract:
Abstract: El objetivo principal de este mini curso es estudiar el conjunto de medidas invariantes por el flujo horocíclico en superficies hiperbólicas. En el caso de una superficie compacta Furstenberg probó que el flujo horocíclico es únicamente ergódico, siendo la medida de Liouville la única medida de probabilidad invariante. En el caso de una superficie de volumen finito Dani probó que toda medida de probabilidad invariante es, o bien la medida de Liouville, o bien una medida soportada en una órbita periódica. En el caso de una superficie geométricamente finita Roblin probó que existe una única medida soportada en todo el conjunto no errante, medida que es infinita. Finalmente, un trabajo reciente de Landesberg y Lindenstrauss clasifican a las medidas invariantes infinitas en el caso de cubrimientos regulares de superficies geométricamente finitas. En este curso se espera probar los resultados de Furstenberg, Dani y Roblin en 3 sesiones. El gran interés de este curso es evidenciar las obstrucciones geométricas que determinan las
distintas clasificaciones en cada caso y dar cuenta de las consecuencias en equidistribución de órbitas periódicas horocíclicas.
Sala 1, Edificio Rolando Chuaqui