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.
Optimal d-Clique Decompositions for Hypergraphs.
Abstract: We determine the optimal constant for the Erdős-Pyber theorem on hypergraphs. Namely, we prove that every n-vertex d-uniform hypergraph H can be written as the union of a family F of complete d-partite hypergraphs such that every vertex of H belongs to at most (n choose d)/(n lg n) graphs in F. This improves on results of Csirmaz, Ligeti, and Tardos (2014), and answers an old question of Chung, Erdős, and Spencer (1983). Our proofs yield several algorithmic consequences, such as an O(n lg n) algorithm to find large balanced...
Random burning of the Euclidean lattice.
Resumen: The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point to set on fire, and the fire propagates constantly at unit speed along the edges of the graph. In joint work with Alice Contat, following Mitsche, Prałat and Roshanbin, we consider two natural random burning procedures in the discrete Euclidean torus $\mathbb{T}_n^d$, in which the points that we set on fire at each step are random variables. Our main...
The Ramsey Number of Multiple Copies of a Graph
Abstract: Let H be a graph without isolated vertices. The Ramsey Number r(nH) is the minimum N such that every coloring of the edges of the complete graph on N vertices with red and blue contains n pairwise vertex-disjoint monochromatic copies of H of the same color. In 1975, Burr, Erdős and Spencer established that r(nH) is a linear function of n for large enough n. In 1987, Burr proved a superexponential upper bound for when the long-term linear behavior starts. In 2023, Bucic and Sudakov showed that the long-term linear behavior starts...
Clearing-out of dipoles for minimisers of 2-dimensional discrete energies with topological singularities.
Abstract: A key question in the analysis of discrete models for material defects, such as vortices in spin systems and superconductors or isolated dislocations in metals, is whether information on boundary energy for a domain can be sufficient for controlling the number of defects in the interior. We present a general combinatorial dipole-removal argument for a large class of discrete models including XY systems and screw dislocation models, allowing to prove sharp conditions under which controlled flux and boundary energy guarantee tohave...
Machine learning-driven COVID-19 early triage and large-scale testing strategies based on the 2021 Costa Rican Actualidades survey.
Resumen: Due to resource limitations, the COVID-19 pandemic presented substantial challenges for large-scale testing. Traditional approaches often fail to balance detection rates with limited reagents and laboratory capacity. In this work we introduced a machine learning–driven triage framework to stratify individuals by contagion risk and deploy adaptive testing protocols accordingly. We adapted the strategies according to the characteristics of RT-PCR tests, which offer high sensitivity, but they require specialized laboratories, and...
Caracterización de relaciones regionalmente proximales mediante el semigrupo envolvente.
RESUMEN: El estudio de los sistemas de orden d ha despertado gran interés por sus aplicaciones en sistemas dinámicos, teoría de números y combinatoria. Un aspecto interesante es el estudio de las propiedades algebraicas de sus semigrupos envolventes. En esta charla se abordará la conexión entre el semigrupo envolvente y la relación regionalmente proximal, la cual define a los sistemas de orden d. En particular, se presentará una caracterización algebraica de estas relaciones. Luego mencionaré aplicaciones de estos resultados a la estructura...
Column Generation and the Feature Selection Problem.
Abstract: Column generation is a well-known decomposition method to solve linear and mixed integer problems with a large number of variables. A similar column generation decomposition method can be constructed for conic optimization problems. In this talk we present work that explores whether this can be a competitive solution method for the continuous relaxation of the feature selection problem.
Poisson representation of Brownian bridge.
Resumen: We consider Brownian motion $(B(t))$, for $t\in[0,1]$, and Brownian bridge $BB(t)$, the Brownian motion conditioned to return to $0$ at time~$1$. The following identity is well known,(1)\,\hfill law of $(BB(t))_{t\in[0,1]}= $ law of $(B(t)- tB(1))_{t\in[0,1]}$. \hfill\ A centered and rescaled Poisson point process $B^\varepsilon(t)$ converges to Brownian motion, where $\varepsilon$ is the scaling parameter going to $0$. For each $\varepsilon>0$, we construct a coupling $(B^\varepsilon(t),BB^\varepsilon (t))$ satisfying an...
The Haagerup property.
Abstract: The Haagerup property is an analytic property of groups that generalises amenability. It originated from the study of C*-algebras, and it has found applications in several areas of mathematics, including harmonic analysis, geometric group theory, topology, and ergodic theory. This talk will consist in an introduction to this property and its connections to group actions on Banach spaces.
Computer-assisted proof of robust transitivity.
RESUMEN: A smooth dynamical system is transitive if it has a dense orbit, loosely meaning that it has some chaos in a topological sense. If this property holds for all diffeomorphisms in a C¹-neighborhood, we say that systems in this neighborhood are robustly transitive. By Bonatti, Diaz and Pujals (2003), robustly transitive diffeomorphisms are volume hyperbolic, and thus they have positive topological entropy, being chaotic in a strict sense and in a robust way. Robust properties are key in classifying smooth dynamical systems, and they are...
