Seminarios

Futuros Eventos

2020-06-18
16:00hrs.
Laten - Seminario Latinoamericano de Teoría de Números
Ariel Pacetti. Universidad de Córdoba
Q Curvas, Modularidad y Problemas Diofánticos
Ingresar aquí para solicitar acceso: http://www.cmat.edu.uy/%7Etornaria/LATeN/
2020-06-10
15:00hrs.
Seminario Núcleo Milenio Midas
Miguel de Carvalho. University of Edinburgh
Elements of Bayesian Geometry
Zoom (Pedir link a Luis Gutiérrez)
Abstract:
In this talk, I will discuss a geometric interpretation to Bayesian inference that will yield a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of the proposed geometry is the observation that the marginal likelihood can be regarded as an inner product between the prior and the likelihood. A key concept in our geometry is that of compatibility, a measure which is based on the same construction principles as Pearson correlation, but which can be used to assess how much the prior agrees with the likelihood, to gauge the sensitivity of the posterior to the prior, and to quantify the coherency of the opinions of two experts. Estimators for all the quantities involved in our geometric setup are discussed, which can be directly computed from the posterior simulation output. Some examples are used to illustrate our methods, including data related to on-the-job drug usage, midge wing length, and prostate cancer. Joint work with G. L. Page and with B. J. Barney.
2020-06-09
13:00hrs.
Seminario de Geometría Algebraica
Alexander Kuznetsov. Steklov Mathematical Institute
Gushel-Mukai Varieties
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiago
https://researchseminars.org/seminar/AG_Santiago
2020-06-09
15:30hrs.
Seminario Teoría de Multiplicación Compleja
Matías Bruna. PUC
Reticulados Con Multiplicaciones Complejas
zoom (pedir invitación a Ricardo Menares)
2020-06-08
16:30hrs.
Seminario de Sistemas Dinámicos
Andrés Navas. Universidad de Santiago de Chile
Distorted Diffeomorphisms and Regularity
Zoom (pedir link a Raimundo Briceño)
2020-06-05
14:00hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de Representaciones de Galois: Representaciones del Grupo de Galois de Un Campo Local
Zoom (pedir link a Héctor Pastén)
2020-06-05
11:00hrs.
Seminario Teoría de Multiplicación Compleja
Javier Reyes. Pontificia Universidad Católica de Chile
Polinomio Modular
zoom (pedir invitación a Ricardo Menares)
http://www.mat.uc.cl/~rmenares/SeminarioCM.html

Eventos Pasados

2020-06-04
16:00hrs.
Laten - Seminario Latinoamericano de Teoría de Números
Gustavo Rama. Universidad de la República
Cálculo de formas paramodulares usando formas modulares ortogonales.
Ingresar aquí para solicitar acceso: http://www.cmat.edu.uy/%7Etornaria/LATeN/
2020-06-03
15:30hrs.
Seminario Teoría de Multiplicación Compleja
Marcos Morales. Pontificia Universidad Católica de Chile
Más sobre el invariante jota, parte II
zoom (pedir invitación a Ricardo Menares)http://www.mat.uc.cl/~rmenares/SeminarioCM.html
2020-06-02
15:30hrs.
Seminario de Teoría de Números
Patricio Pérez. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: Cohomología de Galois
Zoom (pedir link a Héctor Pastén)
2020-06-01
16:30hrs.
Seminario de Sistemas Dinámicos
Aníbal Velozo. Yale University
Suspension flows over countable Markov shifts
Zoom (pedir link a Raimundo Briceño)
2020-05-29
14:00hrs.
Seminario de Teoría de Números
Matías Alvarado. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: Representaciones asociadas a curvas elípticas
Zoom (pedir link a Héctor Pastén)
2020-05-28
16:00hrs.
Laten - Seminario Latinoamericano de Teoría de Números
Amalia Pizarro . Universidad de Valparaíso
Criptografía basada en Isogenias
Abstract:
En 1997, Peter Shor creó un algoritmo cuántico que resuelve en tiempo polinomial el problema del logaritmo discreto y de factorización de números enteros. A partir de ese momento, comienza el interés por desarrollar protocolos criptográficos post-cuánticos (i.e. resistentes a ataques cuánticos). En esta charla, mostraremos un poco del estado del arte de dos protocolos post-cuánticos basados en isogenias de curvas elítpicas supersingulares (SIDH y CSIDH).
Ingresar aquí para solicitar acceso: http://www.cmat.edu.uy/%7Etornaria/LATeN/http://www.cmat.edu.uy/%7Etornaria/LATeN/
2020-05-27
15:00hrs.
Seminario Núcleo Milenio Midas
Nicolás Kuschinski. Pontificia Universidad Católica de Chile
Grid-Uniform Copulas and Rectangle Exchanges: Model and Bayesian Inference Method for a Rich Class of Copula Functions
Abstract:
We introduce a new class of copulas which we call Grid-Uniform Copulas. We show the richness of this class of copulas by proving that for any copula $C$ and any $\epsilon>0$ there is a Grid-Uniform Copula that approximates it within Hellinger distance $\epsilon$. We then proceed to show how Grid-Uniform Copulas can be used to create semiparametric models for multivariate data, and show an elegant way to perform MCMC sampling for these models.

Zoom (Pedir link a Luis Gutiérrez)
2020-05-26
13:00hrs.
Seminario de Geometría Algebraica
Yulieth Prieto. Università Di Bologna
Automorfismos simplécticos en superficies K3
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiagohttps://mathseminars.org/seminar/AG_Santiago
2020-05-26
15:30hrs.
Seminario de Teoría de Números
Santiago Radi. Universidad de la República (Uruguay)
Modularidad de representaciones de Galois: Introducción a las representaciones de Galois
Zoom (pedir link a Héctor Pastén)
2020-05-21
16:00hrs.
Laten - Seminario Latinoamericano de Teoría de Números
Álvaro Lozano-Robledo. University of Connecticut
Una clasificacion de grafos de isogenia-torsion de curvas elipticas sobre Q
Ingresar aquí para solicitar acceso: http://www.cmat.edu.uy/%7Etornaria/LATeN/http://www.cmat.edu.uy/%7Etornaria/LATeN/
2020-05-20
15:45 hrs.
Seminario Fismat
Asaf Levi Franco Arellano. Unam
Operadores de Sturm-Liouville Con Interacciones Puntuales
Abstract:
En esta charla estudiaré la invarianza de los valores propios de operadores de Sturm-Liouville autoadjuntos con interacciones puntuales. En un ambiente probabilístico, dada una familia $H_\omega$ de esta clase de operadores mostraré que un punto es valor propio para toda $\omega$ o solo para un conjunto de $\omega$'s de medida cero.

online seminar with zoom
2020-05-20
15:00hrs.
Seminario Núcleo Milenio Midas
Mauricio Castro. Pontificia Universidad Católica de Chile
Automated learning of t factor analysis models with complete and incomplete data
Abstract:
The t factor analysis (tFA) model is a promising tool for robust reduction of high-dimensional data in the presence of heavy-tailed noises. When determining the number of factors of the tFA model, a two-stage procedure is commonly performed in which parameter estimation is carried out for a number of candidate models, and then the best model is chosen according to certain penalized likelihood indices such as the Bayesian information criterion. However, the computational burden of such a procedure could be extremely high to achieve the optimal performance, particularly for extensively large data sets. In this paper, we develop a novel automated learning method in which parameter estimation and model selection are seamlessly integrated into a one-stage algorithm. This new scheme is called the automated tFA (AtFA) algorithm, and it is also workable when values are missing. In addition, we derive the Fisher information matrix to approximate the asymptotic covariance matrix associated with the ML estimators of tFA models. Experiments on real and simulated data sets reveal that the AtFA algorithm not only provides identical fitting results, as compared to traditional two-stage procedures, but also runs much faster, especially when values are missing.
Zoom (Pedir link a Luis Gutiérrez)
2020-05-19
13:00hrs.
Seminario de Geometría Algebraica
José Ignacio Yáñez. U of Utah
Dimensión númerica de divisores
Abstract:

Un invariante importante en el estudio de la geometría de un divisor es su dimensión de Iitaka. Ésta mide el crecimiento asintótico del espacio de secciones de los múltiplos del divisor. Sin embargo, la dimensión de Iitaka no se comporta bien en relación a la clase numérica del divisor, por lo que se han dado diversas definiciones que buscan capturar facetas de esta dimensión y que no dependan de la clase numérica.

En esta charla presentaré algunas definiciones de dimensión numérica de un divisor, junto con un ejemplo que evidencia problemas con estas definiciones y preguntas que surgen a partir de esto.


Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiagohttps://mathseminars.org/seminar/AG_Santiago
2020-05-15
14:00hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de Representaciones de Galois: La parametrización modular y el rango de una curva elíptica
Zoom (pedir link a Héctor Pastén)www.mat.uc.cl/~natalia.garcia/stn.html
2020-05-14
16:00hrs.
Laten - Seminario Latinoamericano de Teoría de Números
Ricardo Menares . Pontificia Universidad Católica de Chile
Sobre el mínimo esencial de la altura de Faltings
Abstract:

(trabajo en conjunto con José Burgos Gil y Juan Rivera-Letelier): en muchos problemas diofantinos (Manin-Mumford, Bogomolov, André-Oort, etc) resulta útil saber que una familia de puntos algebraicos se equidistribuye. Hay una familia de teoremas de equidistribución que afirman que ``puntos de altura pequeña'' se equidistribuyen. 

Las funciones de altura están diseñadas para medir el tamaño de objetos aritméticos. El ejemplo más simple es la Altura de Weil: dado un número racional x=a/b, la altura de Weil le asocia el valor log max {|a|,|b|}, que más o menos indica el número de dígitos necesarios para escribir x. Más generalmente, cuando x es un número algebraico, la altura de Weil le asocia un número real no negativo que indica cuan grande son, en promedio, los coeficientes del polinomio mínimo. Un teorema de Bilu afirma que una sucesión de conjugados galoisianos de puntos algebraicos con altura de Weil tendiendo a cero, debe equidistribuirse según la medida de Lebesgue en el círculo unitario complejo.

En esta charla nos enfocaremos en el caso de la Altura de Faltings, que mide el tamaño de una curva elíptica definida sobre un cuerpo de números. Faltings introdujo esta función en el contexto de su demostración de la conjetura de Mordell. Esta altura toma en cuenta el lugar de mala reducción de la curva y el conjunto de períodos complejos. Al intentar establecer un análogo del teorema de Bilu en este contexto, el primer obstáculo es entender qué es una sucesión de curvas elípticas pequeñas. En esta charla se explicará en detalle este problema y presentaré algunos resultados parciales.


Ingresar aquí para solicitar acceso: http://www.cmat.edu.uy/%7Etornaria/LATeN/http://www.cmat.edu.uy/%7Etornaria/LATeN/
2020-05-13
15:00hrs.
Seminario Núcleo Milenio Midas
Freddy Palma Mancilla. Universidad Nacional Autónoma de México
Intertwinings for Markov branching processes
Abstract:
Using a stochastic filtering framework we devise some intertwining relationships in the setting of Markov branching processes. One of our result turns out to be the basis of an exact simulation method for these kind of processes. Also, the population dynamic scheme inherent in the model helps to study the behavior of prolific individuals by observing the total size of the population. Moreover, we study a population with two types of immigrations, where it is observed the total immigration, and our objective is to study each immigration separately. This result allows to link continuous-time Markov chains with continuous-state branching (CB) processes.
Zoom (Pedir link a Luis Gutiérrez)
2020-05-13
15:30hrs.
Seminario Teoría de Multiplicación Compleja
Marcos Morales. PUC
Más sobre el invariante jota
zoom (pedir invitación a Ricardo Menares)http://www.mat.uc.cl/~rmenares/SeminarioCM.html
2020-05-12
14:00hrs.
Seminario de Geometría Algebraica
Antonio Laface. U de Concepción
Cox rings and blowing-ups
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiagohttps://mathseminars.org/seminar/AG_Santiago
2020-05-12
15:30hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de Representaciones de Galois: Curvas elípticas modulares
Zoom (pedir link a Héctor Pastén)
2020-05-11
16:30hrs.
Seminario de Sistemas Dinámicos
Nishant Chandgotia. Hebrew University of Jerusalem
Predictive sets
Zoom (pedir link a Raimundo Briceño)
2020-05-08
14:00hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: La construcción de Eichler-Shimura
Zoom (pedir link a Héctor Pastén)
2020-05-06
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Eduardo Cerpa. Instituto de Ingeniería Matemática y Computacional
Propiedades de estabilidad y estabilización para algunos sistemas hiperbólicos
https://reuna.zoom.us/j/402264549
2020-05-06
15:00hrs.
Seminario Núcleo Milenio Midas
Luis Gutiérrez. Pontificia Universidad Católica de Chile
Bayesian nonparametric hypothesis testing procedures
Abstract:
Scientific knowledge is firmly based on the use of statistical hypothesis testing procedures. A scientific hypothesis can be established by performing one or many statistical tests based on the evidence provided by the data. Given the importance of hypothesis testing in science, these procedures are an essential part of statistics. The literature of hypothesis testing is vast and covers a wide range of practical problems. However, most of the methods are based on restrictive parametric assumptions. In this talk, we will discuss Bayesian nonparametric approaches to construct hypothesis tests in different contexts. Our proposal resorts to the literature of model selection to define Bayesian tests for multiple samples, paired-samples, and longitudinal data analysis. Applications with real-life datasets and illustrations with simulated data will be discussed.
Zoom (Pedir link a Luis Gutiérrez)
2020-05-05
14:00hrs.
Seminario de Geometría Algebraica
Sebastian Torres. Umass Amherst
Bott desaparición via GIT y cuantización
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiagohttps://mathseminars.org/seminar/AG_Santiago
2020-05-05
15:30hrs.
Seminario de Teoría de Números
Natalia García. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: El Álgebra de Hecke II
Zoom (pedir link a Héctor Pastén)
2020-05-04
16:30hrs.
Seminario de Sistemas Dinámicos
François Maucourant. Irmar, Université de Rennes 1
Dynamics of unipotent frame flows on hyperbolic manifolds
Zoom (pedir link a Raimundo Briceño)
2020-05-01
14:00hrs.
Seminario de Teoría de Números
Jerson Caro. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: El álgebra de Hecke
Zoom (pedir link a Héctor Pastén)
2020-04-29
15:00hrs.
Seminario Núcleo Milenio Midas
Inés Varas. Pontificia Universidad Católica de Chile
Linking measurements: a Bayesian nonparametric approach
Abstract:
Equating methods is a family of statistical models and methods used to adjust scores on different test forms so that scores can be comparable and used interchangeably. These methods lie on functions to transform scores on two or more versions of a test. Most of the proposed approaches for the estimation of these functions are based on continuous approximations of the score distributions, as they are most of the time, discrete functions. Considering scores as ordinal random variables, we propose a flexible dependent Bayesian nonparametric model for test equating. The new approach avoids continuous assumptions of the score distributions, in contrast to current equating methods. Additionally, it allows the use of covariates in the estimation of the score distribution functions, an approach not explored at all in the equating literature. Applications of the proposed model to real and simulated data under different sampling designs are discussed. Several methods are considered to evaluate the performance of our method and to compare it with current methods of equating. Respect to discrete versions of equated scores obtained from traditional equating methods,  results show that the proposed method has better performance.
Zoom (Pedir link a Luis Gutiérrez)
2020-04-28
15:30hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: Recuento de la teoría de formas modulares y operadores de Hecke
Zoom (pedir link a Héctor Pastén)
2020-04-24
14:00hrs.
Seminario de Teoría de Números
Matías Alvarado. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: Curvas modulares y formas modulares sobre Q
Zoom (pedir link a Héctor Pastén)
2020-04-22
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Adrien Taylor. Centre de Recherche Inria de Paris
Computer-aided worst-case analyses and design of first-order methods for convex optimization
Abstract:
In this presentation, I want to provide a high-level overview of recent approaches for analyzing and designing first-order methods using symbolic computations and/or semidefinite programming. A particular emphasis will be given to the "performance estimation" approach, which enjoys comfortable tightness guarantees: the approach fails only when the target results are impossible to prove. In particular, it allows obtaining (tight) worst-case guarantees for fixed-step first-order methods involving a variety of oracles - that includes explicit, projected, proximal, conditional, mirror, inexact, or stochastic (sub)gradient steps - and a variety of convergence measures. The presentation will be example-based, as the main ingredients necessary for understanding the methodologies are already present in the analysis of the vanilla gradient method. For convincing the audience, and if time allows, we will provide other examples that include analyses of the Douglas-Rachford splitting, and of a variant of the celebrated conjugate gradient method in its most naive form.

The methodology is implemented within the package "PESTO" (for "Performance EStimation TOolbox", available at: https://github.com/AdrienTaylor/Performance-Estimation-Toolbox), which allows using the framework without the SDP modelling steps. This talk are based on joint works with great collaborators (who will be mentioned during the presentation).
https://reuna.zoom.us/j/402264549
2020-04-22
15:00hrs.
Seminario Núcleo Milenio Midas
Diego Morales Navarrete. Pontificia Universidad Católica de Chile
On modeling and estimating geo-referenced count spatial data
Abstract:

Modeling spatial data is a challenging task in statistics. In many applications, the observed data can be modeled using Gaussian, skew-Gaussian or even restricted random field models. However, in several fields, such as population genetics, epidemiology and aquaculture, the data of interest are often count data, and therefore the mentioned models are not suitable for their analysis. Consequently, there is a need for spatial models that are able to properly describe data coming from counting processes. Commonly three approaches are used to model this type of data: GLMMs with gaussian random field (GRF) effects, hierarchical models, and copula models. Unfortunately, these approaches do not give an explicit characterization of the count random field like their q-dimensional distribution or correlation function. It is important to stress that GLMMs and hierarchical models induces a discontinuity in the path. Therefore, samples located nearby are more dissimilar in value than in the case when the correlation function is continuous at the origin. Moreover, there are cases in which the copula representation for discrete distributions is not unique, so it is unidentifiable. Hence to deal with this, we propose a novel approach to model spatial count data in an efficient and accurate manner. Briefly, starting from independent copies of a “parent” gaussian random field, a set of transformations can be applied, and the result is a non-Gaussian random field. This approach is based on the characterization of count random fields that inherit the well-known geometric properties from Gaussian random fields.

 
 

Zoom (Pedir link a Luis Gutiérrez)
2020-04-21
15:30hrs.
Seminario de Teoría de Números
Fernando Herrera. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: Funciones L
Zoom (pedir link a Héctor Pastén)
2020-04-17
14:00hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de Representaciones de Galois: Calculando con formas modulares y operadores de Hecke
Zoom (pedir link a Héctor Pastén)
2020-04-15
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
George G. Vega Yon. Pontificia Universidad Católica de Chile
Predicción de funciones genéticas utilizando evidencia experimental y árboles filogenéticos: Un modelo evolutivo
Abstract:
La predicción de funciones genéticas es un tópico activo en la literatura
bioinformática. Gracias a esfuerzos internacionales como el "Gene
Ontology Project" (GO), investigadores han logrado acumular una
cantidad importante de conocimiento sobre procesos y sistemas
biológicos, incluyendo la manera en que los genes, y nalmente las
especies, se connectan a lo largo de la evolución. En esta presentación
ilustraré una propuesta para modelar la evolución de funciones genéticas
haciendo uso de árboles evolutivos (filogenética) e información
experimental disponibles en el proyecto GO, con el objetivo nal de hacer
predicciones masivas sobre funciones genéticas.
De principio a fin, éste proyecto hace uso de técnicas de ciencia de datos
incluyendo: Manejo de datos grandes ("big data"), computación en
paralelo, y visualización de datos complejos, entre otras.

https://reuna.zoom.us/j/402264549
2020-04-14
15:30hrs.
Seminario de Teoría de Números
Jerson Caro. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: Operadores de Hecke y teoría de Hecke
Zoom (pedir link de la reunión a Héctor Pastén)
2020-04-10
14:00hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de Representaciones de Galois: Curvas modulares y formas modulares sobre C
Zoom (pedir link de la reunión a Jerson Caro)
2020-04-07
15:30hrs.
Seminario de Teoría de Números
Héctor Pastén. Pontificia Universidad Católica de Chile
Modularidad de representaciones de Galois: Curvas elípticas
Abstract:
Seguiremos el libro 
Darmon, Henri; Fred Diamond; Richard Taylor. Fermat’s last theorem
y se expondrá en la medida de lo posible una sección por clase.

Zoom (pedir link de la reunión a Jerson Caro)
2020-03-16
14:00hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Eduardo Friedman. Universidad de Chile
[cancelado] Unconditional discriminant lower bounds exploiting violations of the Generalized Riemann Hypothesis
Abstract:
 



Sala 2
2020-03-13
16:00hrs.
Coloquio de Matemática UC
Carlos Román. UC Chile
El modelo de superconductividad de Ginzburg-Landau
Abstract:
La superconductividad es un fenómeno que ha atraído muchísima atención desde su descubrimiento en 1911 por Onnes. Sus dos características más llamativas son la posibilidad de circulación de corrientes eléctricas sin disipación y la levitación superconductora mediante la expulsión de un campo magnético aplicado. En 1950 Ginzburg y Landau propusieron un modelo fenomenológico para su estudio, el cual ha sido tremendamente exitoso, con varios premios Nobel otorgados por su análisis. En presencia de un campo magnético aplicado, este modelo predice exitosamente la aparición en un superconductor de tipo II de defectos topológicos cuantizados denominados vórtices (similares a los de dinámica de fluidos). En este coloquio describiremos el comportamiento de superconductores de tipo II en diferentes regímenes de intensidad de un campo magnético aplicado y mostraremos las principales herramientas matemáticas para analizar el número e interacción de sus correspondientes vórtices.
auditorio Ninoslav Bralic
2020-03-13
15:00hrshrs.
Seminario de Análisis y Geometría
Karina Vilches. Universidad Católica del Maule
Emergent behaviors in multi-cellular tumor progression including micro-environmental interactions anunciado. Atención: Seminario suspendido por razones de fuerza mayor
Abstract:
Atención: Seminario suspendido por razones de fuerza mayor

We present a mathematical approach that captures and explores a wide range of mechanisms and biological variability in tumor progression to better understand the orchestrate multiple phenomena in cancer dynamics. In this respect, Mathematical Biology is needed to promote the realization of modeling platforms that facilitate the discovery of novel biological phenomena, rules, and theories. Therefore, the main goal of this presentation corresponds to discuss the analysis of a mathematical model that represents a multi-cellular chemotaxis-haptotaxis interaction in Cancer progression. The main novelty consists in applying the non-linear analysis of parabolic-elliptic system and numerical approximation to describe the micro-environment effects over tumor progression.
Sala 1, Facultad de Matemáticas
2020-03-06
16:00hrs.
Club de Matemática
Nicolás Vilches. UC
La teoría de Ramsey y los ataques alienígenas
Abstract:
La teoría de Ramsey es un área muy interesante de la matemática. Es llamativo ver cómo hace relación a temas tan diversos como buscar polígonos convexos en conjuntos de puntos y progresiones monótonas. Es aún más asombroso ver cómo aparece involucrada en matrimonios y ataques alienígenas. En esta charla daremos una breve introducción a algunos de sus resultados y comentaremos acerca de otras vertientes para seguir leyendo.
Ninoslav Bralichttp://clubdematematica.mat.uc.cl/
2020-03-04
14:00hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Eyal Goren. Mcgill University
Complex multiplication - old and new
Abstract:
The theory of complex multiplication is more than a century old; its origins date back to Klein, Hilbert, Kummer, Weber, Deuring and many others. It has been instrumental in the development of class field theory and algebraic number theory. Yet, more than a century later we find new theorems that are truly surprising. 
I will start with this historical perspective and try to position some of these new developments in the light of the André-Oort conjecture - a conjecture in the area of Shimura varieties that was recently resolved by Tsimerman, building on ideas of Edixhoven, Pila, Wilkie and Zannier. The resolution rests on the averaged Colmez conjecture, a conjecture that addresses the arithmetic complexity of abelian varieties with complex multiplication, which was proved by Andreatta-Howard-Madapusi Pera and the speaker, and, independently, by Yuan-Zhang.

Sala 1
2020-01-29
12:00 hrs.
Seminario Núcleo Milenio Midas
José Quinlan. Pontificia Universidad Católica de Chile
On the Support of Yao-based Random Ordered Partitions for Change-Point Analysis
Abstract:

In Bayesian change-point analysis for univariate time series, prior distributions on the set of ordered partitions play a key role for change-point detection. In this context, mixtures of product partition models based on Yao's cohesion are very popular due to their tractability and simplicity. However, how flexible are these prior processes to describe different beliefs about the number and locations of change-points? In this talk I will address the previous question in terms of its weak support.


Sala 1, Facultad de Matemáticas
2020-01-22
15:45 hrs.
Seminario Fismat
Francesco Chiacchio. Universidad de Nápoles
Some isoperimetric problems in the Euclidean space with density
Abstract:
We will discuss the isoperimetric problem for factorized measures obtained as perturbations of the Gaussian and the anti-Gaussian, respectively. Among other things, we will show that some isoperimetric problems, for which balls centered at the origin are stable, have no solutions.Time permitting, some applications, like, for instance, Faber-Krahn type inequalities will be presented too. (Joint works with F. Brock and A. Mercaldo)
Sala 5, Facultad de Matemáticas
2020-01-22
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Karim Johannes Becher. Universiteit Antwerpen
Quadratic forms and diophantine sets
Abstract:
The interplay between valuations and certain geometrically rational varieties, in particular quadrics, has turned out to be very fruitful for proving that certain subsets of fields are existentially definable or diophantine. In particular, this has been used by J. Koenigsmann to prove that $\mathbb{Q}\backslash \mathbb{Z}$ is diophantine in $\mathbb{Q}$. His proof combines several ingredients from classical number theory, involving in particular the Hasse-Minkowski local-global principle for quadratic forms. In my talk I want to highlight some ingredients of proofs for showing that certain subsets of fields are diophantine and some interesting questions for quadratic forms arising from this context.
Sala de Seminarios, Dpto de Matemáticas. Las Palmeras 3425, Universidad de Chile
2020-01-22
10:00hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Diego Izquierdo. École Polytechnique
Lambda-buildings associated to quasi-split groups over Lambda-valued fields
Abstract:
Let $\Lambda$ be a totally ordered abelian group and let $K$ be a Henselian $\Lambda$-valued field. Let $G$ be a quasi-split reductive group over $K$. In 1972, Bruhat and Tits constructed a building on which the group $G(K)$ acts provided that $\Lambda$ is a subgroup of the real numbers. In this talk, we will deal with the general case where there are no assumptions on $\Lambda$ and construct a $\Lambda$-building in the sense of Bennett on which $G(K)$ acts.
Sala de seminarios, Dpto de Matemáticas. Las Palmeras 3425, Universidad de Chile
2020-01-22
12:00 hrs.
Seminario Núcleo Milenio Midas
Miles Ott. Smith College
Respondent-Driven Sampling: Challenges and Opportunities
Abstract:
Respondent-driven sampling leverages social networks to sample hard-to-reach human populations, including among those who inject drugs, sexual minority, sex worker, and migrant populations.  As with other link-tracing sampling strategies, sampling involves recruiting a small convenience sample, who invite their contacts into the sample, and in turn invite their contacts until the desired sample size is reached. Typically, the sample is used to estimate prevalence, though multivariable analyses of data collected through respondent-driven sampling are becoming more common. Although respondent-driven sampling may allow for quickly attaining large and varied samples, its reliance on social network contacts, participant recruitment decisions, and self-report of ego-network size makes it subject to several concerns for statistical inference.  After introducing respondent-driven sampling I will discuss how these data are actually being collected and analyzed, and opportunities for statisticians to improve upon this widely-adopted method.
Sala 1, Facultad de Matemáticas
2020-01-21
16:00hrshrs.
Seminario de Análisis y Geometría
Barbara Brandolini. Departamento de Matemáticas, Universidad de Nápoles, Italia
Improved bounds for Hermite-Hadamard inequalities in higher dimensions
Abstract:
ver pdf
Sala 2, Facultad de Matemáticas
2020-01-15
12:00 hrs.
Seminario Núcleo Milenio Midas
Nicolas Kuschinski. Pontificia Universidad Católica de Chile
FATSO: Una familia de operadores para selección de variables en modelos lineales
Abstract:
En modelos lineales es común encontrarse con situaciones donde varios de los coeficientes de regresión son 0. En estas situaciones, una herramienta común es un operador de selección de variables de tipo "sparsity promoting". El más común de estos operadores es el LASSO, el cual promueve estimaciones en 0. Sin embargo, el LASSO y sus derivados dan poco en términos de parámetros fácilmente interpretables para controlar el grado de selectividad. En esta plática se propondrá una nueva familia de operadores de selección, la cual toma como base la geometría del LASSO, pero que tienen forma analítica distinta, y que dan una manera fácilmente interpretable de controlar el grado de selectividad. Estos operadores corresponden con densidades a priori propias, y por ende se pueden usar para hacer inferencia Bayesiana.
Sala 1, Facultad de Matemáticas
2020-01-14
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Chao Li. Columbia University
On the Kudla-Rapoport conjecture
Abstract:
The classical Siegel-Weil formula relates certain Siegel Eisenstein series with quadratic forms, namely expressing special values of these series as theta functions --- generating series of representation numbers of quadratic forms. The influential program of Kudla aims to establish the arithmetic Siegel-Weil formula, which relates the derivative of certain Siegel Eisenstein series with generating series from arithmetic geometry. We will report a proof of the Kudla-Rapoport conjecture, and discuss its application to L-functions such as generalizations of the Gross-Zagier formula to higher dimension. This is joint work with Wei Zhang.
Sala de Seminarios, Dpto de Matemáticas. Las Palmeras 3425, Universidad de Chile
2020-01-10
14:00hrs.
Seminario de Teoría de Números
Chao Li. Columbia University
Elliptic curves and Goldfeld's conjecture
Abstract:

An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family $y^2=x^3+d$), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our joint work with D. Kriz towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.


Sala 2
2020-01-08
14:00hrs.
Seminario de Geometría Algebraica
Luca Schaffler. University of Massachusetts At Amherst
Compactifications of moduli spaces of algebraic varieties
Abstract:
In algebraic geometry, an algebraic variety is a geometric object defined
by polynomial equations. The space of parameters for a family of algebraic
varieties may also be an algebraic variety called a moduli space. In this
talk oriented to a general audience, I will motivate the study of
compactifications of moduli spaces, focusing on the case of moduli of
polarized K3 surfaces. The original results (joint works with Moon and
Gallardo-Kerr) concern the study of a family of K3 surfaces arising from
eight points in the projective line, and the interplay between different
compactifications of such family coming from Geometric Invariant Theory,
Hodge Theory, and the Minimal Model Program.
sala 2