Noticias en español
Separating the edges of a graph with linearly many subdivisions of K_4.
Abstract: Let G be a graph. As we recall from Ana’s talk, a set S of subgraphs of G is (strongly) separating if for every ordered pair of edges (e,f) in E(G)^2 there exists a subgraph H in S that contains e but not f. Although we traditionally view S as a set of paths, other kinds of separating sets have also been considered. Recently, Botler and Naia proved that every graph can be separated by a set S of subdivisions of K_4 (and lone edges, which are necessary for covering bridges), such that the size of S is a linear function of |V(G)|. This mirrors the corresponding theorem about...
Read MoreTree Embedding Problem for Digraphs.
Abstract: The \textit{tree embedding problem} focuses on identifying the minimal conditions a graph $G$ must satisfy to ensure it contains all trees with $k$ edges. Here, a graph $G$ consists of a set $V$ of elements called vertices, and a set $E$ of (unordered) pairs of vertices, called edges. We say that a graph $G$ is a tree if, for any pair of vertices, there is exactly one path connecting them. Erd\H{o}s and Sós conjectured that any graph $G$ with $n$ vertices and more than $(k-1)n/2$ edges contains every tree with $k$ edges. This conjecture has been generalized into the Antitree...
Read MoreSpectrum of the linearized Vlasov-Poisson system.
Abstract: The Vlasov-Poisson system describes a macroscopic number of particles with their mutual gravitational attraction in a mean-field approximation. Its steady-state solutions are known as “polytropes” and a popular model for galaxies in the astronomy literature. In many cases, they are known to be neutrally stable, but the question of asymptotic stability is widely open. The goal of this talk is to present some results on the linearized equation around a steady state. This is based on joint work with Matías Moreno and Paola Rioseco.
Read MoreSet Selection with Uncertain Weights: Non-Adaptive Queries and Thresholds.
.Abstract: We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal; i.e., they are optimal for every weight that lies within the uncertainty intervals. However, it may be that no universally optimal solution exists, unless we are revealed additional information on the precise values of some elements. In the minimum cost admissible query problem, we are tasked to (non-adaptively) find a minimum-cost subset of...
Read MorePeriodic fractional Ambrosetti-Prodi for one-dimensional problem with drift.
Abstract: We prove Ambrosetti-Prodi type results for periodic solutions of some one-dimensional nonlinear problems that can have drift term whose principal operator is the fractional Laplacian of order s ∈ (0, 1). We establish conditions for the existence and nonexistence of solutions of those problems. The proofs of the existence results are based on the sub-supersolution method combined with topological degree type arguments. We also obtain a priori bounds in order to get multiplicity results. We also prove that the solutions are C1,α under some regularity assumptions in the...
Read MoreCharacterising Retract Subshifts – Introducing The Notion of Contractible Subshift.
RESUMEN: A subshift X is a retract of another subshift Y ⊃ X if the embedding morphism emb: X → Y is split-monic in the category of subshifts (i.e. have a left inverse block-map, or “retract”). To characterise this notion, we introduce “contractibility”, a stregthening of the strong-irreducibility property which requires that the gluings are given by a block-map. After giving the characterisation of being a retract subshift, we will list out a few links between contractibility and other properties of subshifts (e.g. having dense periodic points, having the finite...
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