Noticias en español
Gaussian curvature for LQG surfaces and random planar maps.
Abstract: Liouville quantum gravity is a canonical model for random surfaces conjectured to be the scaling limit of various planar maps. Given that curvature is a central concept in Riemannian geometry, it is natural to ask whether this can be extended to LQG surfaces. Here, we define the Gaussian curvature for LQG surfaces (despite their low regularity) and study the relations with its discrete counterparts. We conjecture that this definition of Gaussian curvature is the scaling limit of the discrete curvature, we prove that the discrete curvature on the $\epsilon$-CRT map with a Poisson...
Read MoreConvergence Analysis of Davis-Yin Splitting via Scaled Relative Graphs.
Abstract: Davis-Yin splitting (DYS) has found a wide range of applications in optimization, but its linear rates of convergence have not been studied extensively. The scaled relative graph (SRG) simplifies the convergence analysis of operator splitting methods by mapping the action of the operator onto the complex plane, but the prior SRG theory did not fully apply to the DYS operator. In this work, we formalize an SRG theory for the DYS operator and use it to obtain tighter contraction factors.
Read MoreCrecimiento 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 la demostración.
Read MorePrecedence 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) distance at most C to the current matching. I will...
Read MoreBalanced 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).
Read MoreSharp 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.
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