Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Distorsión en grupos de difeomorfismos.
Abstract: esta charla discutiremos el concepto de distorsión en grupos. Un elemento de un grupo finitamente generado se dice distorsionado si la métrica de la palabra de sus potencias crece sublineal. Comenzaremos dando una breve introducción, dando un par de ejemplos y luego daremos un par de aplicaciones. Terminaremos planteando y discutiendo una pregunta propuesta por Andrés Navas.
Problem Decomposition in Convex Optimization: Advances Beyond ADMM.
Abstract: Applications of convex optimization in areas like image processing and machine learning have stimulated a huge interest in solution methodology that can take advantage of underlying decomposable structure in a problem, especially when iterations can make good use of “prox” mappings on the problem’s components. Very popular in this development has been the Alternating Direction Method of Multipliers (ADMM). But other approaches that branch out from the same mathematical roots in different modes now offer new...
Opening Pandora’s Box: the Correlated Case.
Abstract: Pandora’s Box models optimization problems where the input consists of stochastic random variables, but the uncertainty can be removed (i.e. reveal the exact value of a variable) by paying an extra price. Our goal is to maximize (or minimize) the price of the variable chosen minus (resp. plus) the cost we paid to learn the exact instantiations of the variables. All previous work on this class of problems assumes that different random variables in the input are distributed independently. Until recently nothing was known for the...
Non-linear stability of hyperbolic collisionless many-particle systems.
Abstract: I will present upcoming non-linear stability results concerning the asymptotic behavior of solutions to classical models arising in kinetic theory. First, I will present an asymptotic stability result for the exterior of the Schwarzschild family of black holes as a solution to the Einstein–massless Vlasov system, assuming spherical symmetry. We exploit the normal hyperbolicity of the trapped set in the black hole exterior to obtain decay in time of the energy momentum tensor. I will also speak about an asymptotic stability...
El grupo de automorfismos de los grafos de fichas de los bipartitos completos.
Abstract: Sea $G$ una gráfica simple de $n$ vértices y $k$ un entero tal que $1\leq k\leq n-1$. El grafo de $k$-fichas, $F_k(G)$, de $G$ es el grafo cuyos vértices son los $k$-conjuntos de vértices de $G$, y donde dos de estos $k$-conjuntos son adyacentes si su diferencia simétrica es una arista de $G$. En esta plática hablaremos sobre la relación que existe entre los grupos de automorfismos de $G$ y de $F_k(G)$. Además, daremos un bosquejo de la prueba para determinar el grupo de automorfismos de $F_k(K_{m,n})$, donde $K_{m,n}$ denota al...
On the duality between height functions and continuous spin systems.
Abstract: We revisit the well known duality relation between integer valued height functions and spin systems with O(2) symmetry. We will apply some simple corollaries from this duality to transfer information from one model to the other. First, we deduce a type of Gaussian domination for the height-function variance. Second, we deduce the monotonicity of this variance with respect to a natural temperature parameter. Finally, we show how “delocalisation” of planar height functions implies a so-called BKT phase transition in the...
Boundary controllability of critically singular parabolic equations on convex domains.
Abstract: In this talk I will discuss the null boundary control of heat-like equations on convex domains, featuring a singular potential that diverges as the inverse square of the distance to the boundary. For this purpose, I will establish global Carleman estimates for the associated operators by combining intermediate inequalities with distinct weights that involve non-smooth powers of the boundary distance. These estimates are sharp in the sense that they capture both the natural boundary conditions and the -energy for the problem....
Scaling limits of individual-based models in adaptive dynamics allowing for local extinction or survival of population.
Abstract: Starting from an individual-based birth-death-mutation-selection model of adaptive dynamics with three scaling parameters (population size, mutation rate, mutation steps size), we will describe several scaling limits that can be applied to this model to obtain macroscopic models of different natures (PDE, stochastic adaptive walks), which allow to characterize long-term evolution of the population. Motivated by biological criticisms on the time-scale of evolution and the absence of local extinctions in the obtained macroscopic...
Percolation games.
Abstract: Inspired by first-passage percolation models, we consider zero-sum games on Z^d and study their limit behavior when the game duration tends to infinity. After reviewing several fundamental results in this literature, we present a generalization and discuss connections with long-term behavior of Hamilton-Jacobi equations.
Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices.
Abstract: We establish analogues of the geometric Pitman 2M−X theorem of Matsumoto and Yor and of the classical Dufresne identity, for a multiplicative random walk on positive definite matrices with Beta type II distributed increments. The Dufresne type identity provides another example of a stochastic matrix recursion that admits an explicit solution.
