Seminarios

Eventos Pasados

2024-01-22
16:00hrs.
Coloquio de Matemática UC
Gunther Uhlmann. University of Washington
Travel Time tomography and boundary rigidity
Abstract:
We will consider the inverse problem of determining the sound speed or
index of refraction of a medium by measuring the travel times of waves
going through the medium. This problem arises in global seismology in
an attempt to determine the inner structure of the Earth by measuring
travel times of earthquakes. It also has several applications in
optics and medical imaging among others.

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

Edificio Villanueva
2024-01-22
11:00hrs.
Seminario de Sistemas Dinámicos
Adrián Esparza. Universidad Austral de Chile
Dominios de Baker hiperbólicos y formalismo termodinámico
Abstract:
Aplicamos técnicas de formalismo termodinámico a una familia de funciones enteras que tiene dominios de Baker de tipo hiperbólico probando la existencia de medidas conformes y obteniendo una fórmula de tipo Bowen para la dimensión de Hausdorff de un subconjunto “dinámicamente bueno” del conjunto de Julia. (Este es un trabajo conjunto con I. Inoquio)
Sala 2
2024-01-18
11:30hrs.
Coloquio de Estadística y Ciencia de Datos de la Pontificia Universidad Católica de Chile
Christian Caamaño . Universidad del Bio-Bio
A flexible Clayton-like spatial copula with application to bounded support data.
Abstract:
The Gaussian copula is a powerful tool that has been widely used to model spatial and/or temporal correlated data with arbitrary marginal distribution. However, this kind of model can potentially be too restrictive since it expresses a reflection symmetric dependence. In this work, we propose a new spatial copula model that allows to obtain random fields with arbitrary marginal distribution with a type of dependence that can be reflection symmetric or not.
Particularly, we propose a new random field with uniform marginal distribution, that can be viewed as a spatial generalization of the classical Clayton copula model. It is obtained through a power transformation of a specific instance of a beta random field which in turn is obtained using a transformation of two independent Gamma random fields.
For the proposed random field we study the second-order properties and we provide analytic expressions for the bivariate distribution and its correlation. Finally, in the reflection symmetric case, we study the associated geometrical properties.
As an application of the proposed model we focus on spatial modeling of data with bounded support. Specifically, we focus on spatial regression models with marginal distribution of the beta type. In a simulation study, we investigate the use of the weighted pairwise composite likelihood method for the estimation of this model. Finally, the effectiveness of our methodology is illustrated by analyzing point-referenced vegetation index data using the Gaussian copula as benchmark. Our developments have been implemented in an open-source package for the R statistical environment.

Keywords: Archimedean Copula, Beta random fields, Composite likelihood, Reflection Asymmetry.
Sala 2
2024-01-18
14:30hrs.
Coloquio de Estadística y Ciencia de Datos de la Pontificia Universidad Católica de Chile
Manuel González. Universidad de la Frontera
Métodos de regularización aplicados a problemas de quimiometría
Sala 2
2024-01-18
15:30hrs.
Coloquio de Estadística y Ciencia de Datos de la Pontificia Universidad Católica de Chile
Daira Velandia. Universidad de Valparaíso
Estimation methods for a Gaussian process under fixed domain asymptotics
Abstract:
This talk will address some inference tools for Gaussian random fields from the increasing domain and fixed domain asymptotic approaches. First, concepts and previous results are presented. Then, the results obtained after studying some extensions of the problem of estimating covariance parameters under the two asymptotic approaches named above are addressed.
Sala 2
2024-01-15
16:30hrs.
Seminario de Sistemas Dinámicos
Borys Kuca. Jagiellonian University
Multiple ergodic averages along polynomials for systems of commuting transformations
Abstract:
The last 50 years have seen tremendous activity at the interface between ergodic theory, combinatorics and number theory that started with Furstenberg’s dynamical proof of the Szemerédi theorem from the 1970s. The goal of this line of research has been to prove new multiple recurrence results and then deduce combinatorial corollaries. To achieve this, one wants to understand the limiting behaviour of relevant multiple ergodic averages. Of particular interest are averages of commuting transformations with polynomial iterates: they play a central role in the polynomial Szemerédi theorem of Bergelson and Leibman. While their norm convergence has been established in a celebrated paper of Walsh, little more has been known for a long time about the form of the limit. In this talk, I will present some recent results on the limits of such averages obtained jointly with Nikos Frantzikinakis and explain how they can be used to answer a number of previously intractable problems at the intersection between ergodic theory and combinatorics.
Sala de Seminarios 7° Piso, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
2024-01-12
13:00hrs.
Seminario de Ingeniería Matemática y Computacional
Brendan Keith. Division of Applied Mathematics, Brown University
Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints
Abstract:
The proximal Galerkin finite element method is a high-order, nonlinear numerical method that preserves the geometric and algebraic structure of bound constraints in infinite-dimensional function spaces. In this talk, we will introduce the proximal Galerkin method and apply it to solve free-boundary problems, enforce discrete maximum principles, and develop scalable, mesh-independent algorithms for optimal design. The proximal Galerkin framework is a natural consequence of the latent variable proximal point (LVPP) methodology, which is a stable and robust alternative to the interior point method that will also be introduced in this talk. LVPP can be viewed as a low-iteration complexity, infinite-dimensional optimization algorithm that may be viewed as having an adaptive barrier function that is updated with a new informative prior at each (outer loop) optimization iteration. One of the main benefits of this algorithm is witnessed when analyzing the classical obstacle problem. Therein, we find that the original variational inequality can be replaced by a sequence of semilinear partial differential equations (PDEs) that are readily discretized and solved with, e.g., high-order finite elements. Throughout the talk, we will arrive at several unexpected contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and an infinite-dimensional Lie group; and (3) a gradient-based, bound-preserving algorithm for two-field density-based topology optimization. The complete latent variable proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. This is joint work with T.M. Surowiec.

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

Sala Multiuso 1° piso /1https://sites.google.com/view/topolodias-stgo/home
2024-01-09
14:50 - 16:00hrs.
Seminario de Geometría Algebraica
Jonny Evans. University of Lancaster
Mini-curso en Topolodías en Santiago: Singularidades y topología I
Sala Multiuso 1° piso /1https://sites.google.com/view/topolodias-stgo/home
2024-01-08
16:30hrs.
Seminario de Sistemas Dinámicos
Neil Mañibo. Universität Bielefeld
Uniquely ergodic subshifts over compactifications of the naturals
Abstract:
In this talk, we will discuss one-dimensional substitution subshifts over (infinite) compact alphabets and their dynamical properties. As a motivating class, we will focus on shifts generated by a parametrised family of substitutions on certain compactifications of the natural numbers. We will provide a general checkable condition for unique ergodicity that relies on compactness properties of the substitution operator, which the analogue of the substitution matrix for infinite alphabets. This is based on joint work with Dan Rust and Jamie Walton, and Dirk Frettloeh and Alexey Garber.
Sala de Seminarios 7° Piso, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile
2024-01-08
12:20hrs.
Facultad
Mauricio Bustamante. PUC
Topolodías en Santiago https://sites.google.com/view/topolodias-stgo/programa
Abstract:
Tendremos charlas en las que se presentarán algunos de los prerrequisitos para seguir el minicurso que imparte Jonny Evans. Luego continuaremos con el minicurso en sí y ponencias sobre temas relacionados.

https://sites.google.com/view/topolodias-stgo/programa
sala de usos múltiples 1. Primer piso del edificio Felipe Villanueva.https://sites.google.com/view/topolodias-stgo/programa
2024-01-08
11:00 hrs hrs.
Facultad
Felipe Riquelme . Pontificia Universidad Católica de Valparaíso (Pucv)
Medidas invariantes para el flujo horocíclico
Abstract:
Abstract: El objetivo principal de este mini curso es estudiar el conjunto de medidas invariantes por el flujo horocíclico en superficies hiperbólicas. En el caso de una superficie compacta Furstenberg probó que el flujo horocíclico es únicamente ergódico, siendo la medida de Liouville la única medida de probabilidad invariante. En el caso de una superficie de volumen finito Dani probó que toda medida de probabilidad invariante es, o bien la medida de Liouville, o bien una medida soportada en una órbita periódica. En el caso de una superficie geométricamente finita Roblin probó que existe una única medida soportada en todo el conjunto no errante, medida que es infinita. Finalmente, un trabajo reciente de Landesberg y Lindenstrauss clasifican a las medidas invariantes infinitas en el caso de cubrimientos regulares de superficies geométricamente finitas. En este curso se espera probar los resultados de Furstenberg, Dani y Roblin en 3 sesiones. El gran interés de este curso es evidenciar las obstrucciones geométricas que determinan las
distintas clasificaciones en cada caso y dar cuenta de las consecuencias en equidistribución de órbitas periódicas horocíclicas.
Sala 1, Edificio Rolando Chuaqui
2024-01-04
11:00 hrshrs.
Facultad
Felipe Riquelme. Pontificia Universidad Católica de Valparaíso (Pucv)
Medidas invariantes para el flujo horocíclico
Abstract:
Abstract: El objetivo principal de este mini curso es estudiar el conjunto de medidas invariantes por el flujo horocíclico en superficies hiperbólicas. En el caso de una superficie compacta Furstenberg probó que el flujo horocíclico es únicamente ergódico, siendo la medida de Liouville la única medida de probabilidad invariante. En el caso de una superficie de volumen finito Dani probó que toda medida de probabilidad invariante es, o bien la medida de Liouville, o bien una medida soportada en una órbita periódica. En el caso de una superficie geométricamente finita Roblin probó que existe una única medida soportada en todo el conjunto no errante, medida que es infinita. Finalmente, un trabajo reciente de Landesberg y Lindenstrauss clasifican a las medidas invariantes infinitas en el caso de cubrimientos regulares de superficies geométricamente finitas. En este curso se espera probar los resultados de Furstenberg, Dani y Roblin en 3 sesiones. El gran interés de este curso es evidenciar las obstrucciones geométricas que determinan las
distintas clasificaciones en cada caso y dar cuenta de las consecuencias en equidistribución de órbitas periódicas horocíclicas.
Sala 1, Edificio Rolando Chuaqui
2024-01-04
16:10hrs.
Seminario de Análisis y Geometría
Cristian González Riquelme. Instituto Superior Tecnico, Lisbon
How regular is the maximal function of a given function?
Abstract:
Maximal operators are a central object in harmonic analysis. The regularity theory of such objects has been an object of study formany authors over the last decades. However, even in the one dimensional case, there are still interesting questions that remain open. In this talk, we will discuss recent developments and open questions about this topic, particularly about the boundedness and continuity for such operators at the derivative level and regularity improving properties of these operators.
Sala Multiuso 1° piso, edificio Felipe Villanueva
2024-01-03
11:00 hrs hrs.
Facultad
Felipe Riquelme . Pontificia Universidad Católica de Valparaíso (Pucv)
Medidas invariantes para el flujo horocíclico
Abstract:
Abstract: El objetivo principal de este mini curso es estudiar el conjunto de medidas invariantes por el flujo horocíclico en superficies hiperbólicas. En el caso de una superficie compacta Furstenberg probó que el flujo horocíclico es únicamente ergódico, siendo la medida de Liouville la única medida de probabilidad invariante. En el caso de una superficie de volumen finito Dani probó que toda medida de probabilidad invariante es, o bien la medida de Liouville, o bien una medida soportada en una órbita periódica. En el caso de una superficie geométricamente finita Roblin probó que existe una única medida soportada en todo el conjunto no errante, medida que es infinita. Finalmente, un trabajo reciente de Landesberg y Lindenstrauss clasifican a las medidas invariantes infinitas en el caso de cubrimientos regulares de superficies geométricamente finitas. En este curso se espera probar los resultados de Furstenberg, Dani y Roblin en 3 sesiones. El gran interés de este curso es evidenciar las obstrucciones geométricas que determinan las
distintas clasificaciones en cada caso y dar cuenta de las consecuencias en equidistribución de órbitas periódicas horocíclicas.
Sala 1, Edificio Rolando Chuaqui