Noticias en español
Exact positive codegree thresholds for perfect matching.
Abstract: Rödl, Ruciński and Szemerédi found best-possible codegree conditions that force the existence of perfect matchings in $k$-graphs. Given that the codegree is too strong for many applications, we study this question for a weaker, but more versatile degree condition, which maintains the codegree’s constructive power: the positive codegree. For a $k$-graph, this corresponds to the minimum degree over all sets of size $k-1$ with degree at least one. For $k\geq 3$ , we show exact minimum positive codegree conditions for the existence of perfect matchings in $k$-graphs with no...
Read MoreAn artificial intelligence method to find extremizers in classical Strichartz inequalities.
Abstract: In this talk we present a new method where machine learning provides clues for the discovery of extremizers in several unsolved Strichartz inequalities appearing in classical problems of Harmonic Analysis. This method is primarily based (but not bounded to) Physics Informed Neural Networks (PINNs), with a novel use of the minimization procedure. We provide several examples of critical points and extremizers found by this method, expecting that some of them are proved as correct solutions to the theoretical minimization problem. This is joint work with R. Freire (DIM) and C. Muñoz...
Read MoreThe Rawlsian Prophet: Max-Min Fair Online Allocation.
Abstract: Prophet inequalities are a central framework in online stochastic decision making, comparing online algorithms to an omniscient benchmark. The utilitarian objective of maximizing expected total value is well understood, with tight competitive ratios across full-information, sample-based, and combinatorial settings. We study prophet inequalities under Rawlsian max-min fairness objectives, and distinguish between two natural notions of fairness: ex-ante and ex-post. The former aims to maximize the minimum expected value, while the latter seeks to maximize the expected minimum value....
Read MoreCompartmental Models for Infectious Diseases: Structure, Intervention, and Applications.
Abstract: Compartmental models have become a fundamental tool for understanding the spread of infectious diseases and evaluating the potential impact of public health interventions. By dividing populations into epidemiological classes and describing transitions between them, these models provide a flexible mathematical framework for studying disease dynamics across a wide range of contexts. In this talk, I will present an overview of compartmental modeling for infectious diseases, including model formulation, qualitative analysis, intervention strategies, and interpretation of outcomes....
Read MorePoisson-Voronoi percolation in high dimensions.
Resumen: We consider a Poisson point process with constant intensity in $ \mathbb{R}^d $ and independently color each cell of the resulting random Voronoi tessellation black with probability $ p $. The critical probability $ p_c(d) $ is the value for $ p $ above which there exists almost surely an unbounded black component and almost surely does not for values below. In this talk I aim to give an overview of the model and sketch some ideas of a proof that $ p_c(d)=(1+o(1)) e d^{-1} 2^{-d} $, as $ d\to\infty $. We also obtain the corresponding result for site percolation on the...
Read MoreRainbow trees and graceful labellings.
Abstract: A tree T on n vertices is said to be graceful if there exists a bijective labelling f of its vertices to the set {1,2,…,n} such that the values of |f(x)-f(y)| are pairwise distinct over all edges xy in E(T), or equivalently, such that the set {|f(x)-f(y)| : xy in E(T)} has size exactly n-1. The longstanding graceful tree conjecture, posed by Rósa in the 1960s, asserts that every tree is graceful. We prove an approximate version of this conjecture by showing that every tree T on n vertices has a bijective labelling f of its vertices to the set {1,2,…,n} such that the set...
Read More