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.
Sistema de Alerta RPF
Seminarios de la Alianza Copernicus-Chile Titulo Sistema de Alerta RPF Expositor Roberto Tapia Servicio Agrícola y Ganadero SAG Fecha: Lunes 15 de Abril de 2019 Hora inicio: 16:00 horas Lugar: Sala Multimedia, Centro de Modelamiento Matemático, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile. Beauchef 851, Santiago – Edificio Norte, Piso 6 Se sugiere entrar por 7 piso y bajar por la escalera (ya que este acceso no requiere tarjeta de entrada) Participación en Linea:...
Set-based Lagrangean decomposition methods for mathematical programming
Abstract: We present generic Lagrangean frameworks for primal (variable) and dual (constraint) decomposition algorithms for nonlinear mathematical programs with generalized inequalities. Akin to the Dantzig-Wolfe (DW) method and the Benders Decomposition (BD), we solve a succession of restricted problems/Lagrangean relaxations in a primal setting or relaxed problems/second stage problems in a dual standpoint. Our approach is generic in the sense that it takes as user-defined inputs 1) a structured subset of the primal (dual)...
A critical Poincaré-Sobolev inequality.
Abstract: We study a specific Poincaré-Sobolev inequality in bounded domains, that has recently been used to prove a semi-classical bound on the kinetic energy of fermionic many-body states. The corresponding inequality in the entire space is precisely scale invariant and this gives rise to an interesting phenomenon. Optimizers exist for some (most ?) domains and do not exist for some other domains, at least for the isosceles triangle in two dimensions. In this talk, I will discuss bounds on the constant in the inequality and the...
On subsets with no arithmetic progressions
ABSTRACT For $N\in \mathbb{N}$, let $\nu(N)$ be the maximal cardinality of a subset of \{1,\ldots,N\} that contains no arithmetic progression of length 3. Finding upper and lower bounds for $\nu(N)$ has been a challenging problem for decades. In this talk I will survey this problem and present a proof of a theorem by Behrend in the 40’s, that gave a surprising lower bound to $\nu(N)$.
Counting problem on infinite periodic billiards and translation surfaces
ABSTRACT The Gauss circle problem consists in counting the number of integer points of bounded length in the plane. This problem is equivalent to counting the number of closed geodesics of bounded length on a flat two dimensional torus or, periodic trajectories, in a square billiard table. Many counting problems in dynamical systems have been inspired by this problem. For 30 years, the experts try to understand the asymptotic behavior of closed geodesics in translation surfaces and periodic trajectories on rational billiards. (Polygonal...
An Introduction to Unstructured Mesh Generation and Adaptation
Abstract: Analytic solutions for most PDEs are known only for some simple domains, such as a circle, square, or sphere. In order to obtain solutions for more realistic domains, numerical approximations such as the finite element method (FEM) and finite volume methods (FVM) are used. Mesh generation is a key step prior to these numerical methods. It is itself an active research topic with background in mathematics, computer science, and engineering. Apart from numerical solution of PDEs, its applications are numerous and have practical uses in...
“On the non-local Lazer-McKenna conjecture with superlinear potential under a partial symmetry condition on the domain: Critical and supercritical cases”
Abstract: “In 1983 A. Lazer and P.J. McKenna conjectured that the Ambrosetti-Prodi type problems have an unbounded number of solutions as a defined parameter grows to infinity. There were not results on this conjecture, other than the one dimensional case, until 2003 by Breuer . In this talk we will see the existence of a family of solutions indexed by a real number for the non-local problem with superlinear potential under a partial symmetry condition on the domain”
Maximizing Covered Area in a Euclidean Plane with Connectivity Constraint
Abstract: Given a set of unit disks in the plane and an integer K, the maximum area connected subset problem asks for a subset of K disks covering the maximum area, under the constraint that the area covered by the K disks is connected. This problem is motivated by wireless router deployment and is a special case of maximizing a submodular function under a connectivity constraint.
Understanding physical mixing processes via transfer operator approach
ABSTRACT: Industrial and chemical mixing processes of various kinds occur throughout nature and are vital in many technological applications.In the context of discrete dynamical systems, the transfer operator approach has been shown as a powerful tools from both theoretic and numerical viewpoint. In this talk, I will use a toy model (i.e., the one dimensional stretch and fold map) as an example to provide a brief introductionon the relationships between the spectral properties of the associated transfer operator and the estimations of the...
