Seminars

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.

 

Unique continuation for some nonlinear dispersive models

Event Date: Jul 31, 2019 in Differential Equations, Seminars

ABSTRACT : This talk is concerned with unique continuation properties (UCP) for solutions to some time evolution equations. We shall study two types of UCP (1) local and (2) asymptotic at infinity. Roughly, (1) local means : If u, v are solutions of the equation which agree in an open set D, then they are identical in the whole domain of definition. Roughly, (2) asymptotic at infinity means if u, v are solutions such that ||| u(t)-v(t)|||<\Infty for t=t_1,and t=t_2, then they are identical in the whole domain of definition. The class of...

ODE blowup on an arbitrary compact set for semilinear dispersive and wave equations

Event Date: Jul 31, 2019 in Dynamical Systems, Seminars

ABSTRACT: We consider the focusing energy subcritical nonlinear wave equation and a Schrödinger equation with nonlinear source term. Given any compact set K, we construct finite energy solutions which blow up at t=0 exactly on K. References: https://arxiv.org/abs/1906.02983 https://arxiv.org/abs/1812.03949

Continuidad de los exponentes de Lyapunov para cociclos lineales no uni- formemente fiber bunched

Event Date: Jul 22, 2019 in Dynamical Systems, Seminars

RESUMEN:   Consideramos una din ́amica fija en la base y estudiamos como los expo- nentes de Lyapunov varian con respecto al cociclo. La continuidad de los exponentes de Lyapunov fue probada por Backes, Brown y Butler para el caso en que el cociclo admite holonom ́ıas estables e inestables uniformes. En este trabajo presentamos un resultado parcial de la conjetura de Marcelo Viana que formula que ser ́ıa suficiente una u ́nica holonom ́ıa uniforme para garantir continuidad. Este es un trabajo en conjunto con Karina Marin...

Distorsión asintótica e invariante de Mather para difeomorfismos

Event Date: Jul 08, 2019 in Dynamical Systems, Seminars

ABSTRACT En esta charla abordaré el concepto de distorsión asintótica de difeomorfismos del intervalo, introducida y explotada anteriormente para el caso del círculo. En particular, discutiré tres resultados obtenidos en colaboración con Hélène Eynard-Bontemps: 1) La distorsión asintótica de un difeomorfismo de puntos fijos parabólicos corresponde a la variación del logaritmo de la derivada de su invariante de Mather; en particular, un difeomorfismo de invariante de Mather no trivial no puede ser distorsionado en el grupo de los...

Modeling energy markets with bilevel games

Event Date: Jul 03, 2019 in Optimization and Equilibrium, Seminars

Abstract: Once upon a time, electricity was merely a fairy tale. Since it has been mastered and distributed though, ensuring the supply-demand balance has always been a challenge. Instead of constantly adapting the production to the demand, a new approach consisting in adapting the demand to the production arose about thirty years ago. This approach is called demand-side management, and can be applied through various techniques, notably pricing: offering time-dependent electricity prices can influence the demand. After a small introduction on...

The Avalanche Principle and Negative Curvature

Event Date: Jul 01, 2019 in Dynamical Systems, Seminars

ABSTRACT: In 2001, M. Goldstein and W. Schlag introduced the Avalanche Principle, a quantitative sufficient condition for the operator norm  $\|A_N\cdots A_1\|$ of a product of matrices in $\mathrm{SL}_2(\mathbb{R})$, to being similar to the product $\|AN\|\cdots \|A_1\|$. Since then several refinements and generalizations have  appeared in the literature.  In this talk I will present a reformulation of this principle in terms of the geometry of the hyperbolic plane, and show how to extend it to metric spaces of negative curvature....

Theorems of Borsuk-Ulam Type

Event Date: Jun 27, 2019 in Dynamical Systems, Optimization and Equilibrium, Seminars

Abstract: The Borsuk-Ulam Theorem states that for any continuous function f from S^n to R^n there is some x in S^n such that f(x) = f(-x).   Replace S^n by the boundary of some open set A of E=R^{n+1} and replace R^n by some n dimensional manifold B. The conclusion of the theorem remains, with the pair x, -x replaced by some x,y on the boundary whose convex combinations contain some fixed point z in the interior of that open set. Indeed there is a topological structure to all such solutions when the z is considered a variable. If B is not a...