# Seminarios

## Futuros Eventos

2017-08-10
17:00hrs.
Seminario de Teoría Espectral
Soeren Fournais. Aarhus Universiy
Tba
Sala 1
2017-07-28
15:30hrs.
Seminario de Pregrado en Matemáticas
Eduardo Oregón . PUC
El Plano Hiperbólico
Sala 1
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.

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
17:00hrs.
Seminario de Pregrado en Matemáticas
Gabriel Ramírez Raposo. PUC
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
2017-07-21
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
14:00-15:20hrs.
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
2017-07-20
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
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
2017-07-20
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
2017-07-19
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
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
2017-07-19
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
2017-07-14
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.
Learning Spaces
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.
Learning Spaces
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.
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
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
2017-07-06
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
2017-07-04
14:00hrs.
Learning Spaces
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.
2017-07-04
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
2017-06-30
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
2017-06-30
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
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
12:00 hrshrs.
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
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
2017-06-29
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/
2017-06-29
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
2017-06-28
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
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.
Learning Spaces
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
2017-06-27
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.
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/
2017-06-23
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
2017-06-23
12:00hrs.
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
2017-06-22
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.
Learning Spaces
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
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
2017-06-16
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
2017-06-15
15:30hrs.
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.
Learning Spaces
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.
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.
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.
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
Las matemáticas en la lucha contra enfermedades infecciosas
Abstract:
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.
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.
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.
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
11:30hrs.
Learning Spaces
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 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
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
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
2017-05-12
16:00 - 17:00hrs.
Seminario de Geometría Algebraica
Sönke Rollenske. U Marburg
Geometry of Stable Surfaces II
Sala 2, Facultad de Matemáticas
2017-05-10
11:20hrs.
Learning Spaces
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
2017-05-10
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
14.30hrs.
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
2017-05-09
16:00hrs.
Seminario de Análisis y Geometría
Suspendido. PUC
SUSPENDIDO
Sala 2, Facultad de Matemáticas UC
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/
2017-05-08
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
2017-05-05
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
2017-05-05
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
2017-05-04
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
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
2017-05-02
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
2017-04-27
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.
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.
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
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
2017-04-25
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
2017-04-24
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
2017-04-24
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
2017-04-21
12:00hrs.
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
16hrs.
Coloquio de Matemática UC
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
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
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.
2017-04-12
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
2017-04-10
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
14:30hrs.
Seminario de Geometría Algebraica
José Ignacio Yáñez. PUC
Pares log canonical y teorema del Cono
Sala 2 PUC
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
2017-04-06
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
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
2017-03-29
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
2017-03-28
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.
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
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
2017-01-13
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
2017-01-12
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.
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.
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
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
2017-01-09
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
2017-01-06
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