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.
Minimal configurations for Frenkel-Kontorova model on a quasicrystal.
RESUMEN: The Frenkel-Kontorova model is a physical model that is mathematically simple to describe and universal in the sense that it can be used to describe several underlying physical concepts. It was originally introduced in 1938 to represent the structure and dynamics of a crystal lattice in the vicinity of a dislocation core. It models a chain of classical particles coupled to their neighbors and subjected to an external potential. In this talk, I will present an overview of some known properties and open questions concerning equilibrium...
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...
On the reachable space for the heat equation.
RESUMEN: The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system $y’ = Ay + Bu$, where $A$ is an operator generating a $C^0$ semigroup $(exp(tA))_{t\geq 0}$ on a Hilbert space $X$, and $B$ is a control operator, for instance a linear operator from an Hilbert space $U$ to $X$, and let us assume that this system is null-controllable...
Set 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...
Characterising 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...
Periodic 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...
Selection principles for the N-BBM and the Fleming-Viot particle system.
Resumen: The selection problem is to show, for a given branching particle system with selection, that the stationary distribution for a large but finite number of particles corresponds to the travelling wave of the associated PDE with minimal wave speed. This had been an open problem for any such particle system. The N-branching Brownian motion with selection (N-BBM) is a particle system consisting of N independent particles that diffuse as Brownian motions in $\mathbb{R}$, branch at rate one, and whose size is kept constant by removing the...
