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.**

## “Mathematical Modelling in school, teacher education and engineering education” (Modelamiento matemático en la escuela y en la formación de profesores y de ingenieros).

Resumen: In this workshop the basic theoretical aspects on the teaching and learning of mathematical modelling in school and teacher as well as engineering education are stressed. Thereby, different levels of mathematics are discussed with respect to the necessity of modifying the modelling process. The participants will also work on a modelling problem, which can be used in schools as well as teacher education. Furthermore, the important aspect of modelling competency and how this can be promoted is presented as well. En este taller se...

## Convex hierarchies, scheduling and symmetries

Abstract: The Sum of Squares (SoS) hierarchy provides a finite nested family K_1, K_2, … , K_n of convex relaxations for an integer program with n variables, that reaches the integer hull, i.e., K_n corresponds to the convex hull of the integer feasible solution. A natural question is to understand how the integrality gap evolves over the family. In particular, a rapid decay of the gap might yield good approximation algorithms. We show that for the classic problem of scheduling identical machines to minimize the makespan, the SoS hierarchy...

## Dispersive blow-up and persistence properties for the Schrödinger-Korteweg-de Vries system.

Abstract: In this talk, we shall prove the existence of dispersive blow-up for the Schrödinger-Korteweg-de Vries system. Roughly, dispersive blow-up has being called to the development of point singularities due to the focussing of short or long waves. In mathematical terms, we show that the existence of this kind of singularities is provided by the linear dispersive solution by proving that the Duhamel term is smoother. This result is the first one regarding systems of nonlinear dispersive equations. To obtain our results we use, in...

## The Ising model from the eyes of the Gaussian free field.

Abstract: The Ising model may be one of the most studied objects of statistical Physics. In recent years, it was shown that a proper renormalisation of a planar Ising model converges to a universal field: the continuous magnetisation field. This field is not a function but a Schwartz distribution, furthermore its statistics are not Gaussian. In this talk, we will study the properties of the Wick product of two independent magnetisation fields and show that they have the same law as a certain trigonometric function of the GFF. We will show how...

## Profile of touch-down solution to a non-local MEMS model

Abstract: In this talk, I am at showing the construction of solutions with extinction (touch-down) for the equation of MEMS devices (Micro-electromechanical systems). In addition to that, we also describe the asymptotic behavior of the solution at the extinction domain.

## Connecting orbits in Hilbert spaces and applications to P.D.E.

Abstract: Functional Analysis methods are often useful to solve efficiently P.D.E. problems. The idea is to view a solution of a P.D.E. as a map with values in a space of functions, and reduce the initial P.D.E. to an O.D.E. problem. I will establish a general theorem on the existence of heteroclinic orbits in Hilbert spaces. As a first application, I will present a new construction, in a more general setting, of the heteroclinic double layers (initially constructed by Schatzman). As a second application, I will show the existence of the...

## Herramientas para gestión de incendios

Seminarios de la Alianza Copernicus-Chile Titulo Herramientas para gestión de incendios Expositor Jordi Brull Corporación Nacional Forestal CONAF. Fecha: lunes 19 de agosto 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:...

## Existence of infinitely many solutions for the Einstein-Lichnerowicz system

Abstract: “We will consider in this talk the Einstein-Lichnerowicz system of equations. It originates in General Relativity as a way to determine initial-data sets for the evolution problem. This system takes the form of a strongly coupled, supercritical, nonlinear system of elliptic PDEs. We will investigate its blow-up properties and show that, under some assumptions on the physics data, it possesses a non-compact family of solutions. This family of solutions will be constructed by combining toplogical methods with a...