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.
Crecimiento de la derivada para difeomorfismos del intervalo (con todos sus puntos fijos parabólicos)
RESUMEN:Hace un par de décadas, Polterovich y Sodin probaron un sorprendente resultado: para un difeomorfismo de clase C² del intervalo con todos sus puntos fijos parabólicos, el crecimiento de la derivada es a lo más cuadrático. En esta charla, comenzaremos comentando aspectos sobre la demostración de este resultado. Luego, estableceremos nuestro resultado principal, el cual ofrece un mejoramiento del resultado de Polterovich y Sodin al estimar exactamente el crecimiento de la derivada. Hablaremos brevemente de las herramientas utilizadas en...
Precedence Constraint Matching.
Abstract: In the precedence-constrained perfect matching problem, one needs to incrementally build a matching, whereby the order in which edges join the matching is subject to precedence constraints. Given a graph G = (V, E), a precedence constraint is a pair (X, e) with e being an edge and X a set of vertices, meaning that e may only be added to the matching after covering at least one vertex in X. In this talk, I will introduce C-canonical precedence constraints, where an edge may join a matching if both end-vertices have (shortest path)...
The Shrinking Target Problem for Self-Affine Sets.
RESUMEN The shrinking target problem involves a dynamical system on a probability space or metric space and the set of starting points of orbits which hit a set of shrinking (defined in a suitable sense) sets infinitely often. Typical questions, depending on the setting, are to try and obtain a 0-1 law for the measure of the set based on the rate the targets shrink and to investigate the Hausdorff dimension of the set. We look at the dimension problem in the case of self-affine sets in R^2. By considering a toy model we will show the...
Balanced excited random walk.
Resumen: We introduce the balanced excited random walk and review recent results. In particular we give non-trivial upper and lower bounds on the range of the balanced excited random walk in two dimensions, and verify a conjecture of Benjamini, Kozma and Schapira. These are the first non-trivial results for the 2-dimensional model. This talk is partially based on a joint work with Omer Angel (University of British Columbia) and Mark Holmes (University of Melbourne).
Sharp Fourier restriction over finite fields.
Abstract: Fourier sharp restriction theory has been a topic of interest over the last decades. On the other hand, efforts have been made in order to develop the theory of Fourier restriction over finite fields. In this talk, we will present some recently made developments (in a joint work with Diogo Oliveira e Silva) in the intersection of these two topics.
Bounds on the approximation error for Deep Neural Networks applied to dispersive models: Nonlinear waves.
Abstract: In this talk we present a comprehensive framework for deriving rigorous and efficient bounds on the approximation error of deep neural networks in PDE models characterized by branching mechanisms, such as waves, Schrödinger equations, and other dispersive models. This framework utilizes the probabilistic setting established by Henry-Labordère and Touzi. We illustrate this approach by providing rigorous bounds on the approximation error for both linear and nonlinear waves in physical dimensions d = 1, 2, 3, and analyze their...
On the nonexistence of NLS breathers.
Abstract: In this talk, we will show a proof of the nonexistence of breather solutions for NLS equations. By using a suitable virial functional, we are able to characterize the nonexistence of breather solutions by only using their inner energy and the power of the corresponding nonlinearity of the equation. We extend this result for several NLS models with different power nonlinearities and even the derivative NLS equation.
