All posts by gnornberg

TBA

Speaker: Matias Moreno

University of Chile

Date: Tuesday, November 29, 2022 at 12 Santiago time

Abstract: TBA

Venue: Online via Zoom / Sala multimedia CMM, 6th floor, Beauchef 851
Chair: Hanne Van Den Bosch

TBA

Speaker: Tomas Andrade

Date: Tuesday, November 22, 2022 at 12 Santiago time

Abstract: TBA

Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Hanne Van Den Bosch

Inverse scattering for critical semilinear wave equations

Speaker: Gunther Uhlmann

University of Washington

Date: Tuesday, October 6, 2022 at 2 p.m. Santiago time

Abstract: In inverse scattering ione attempts to find the properties of a medium
by making remote observations. It has applications in physics,
geophysics, medical imaging, non-destructive evaluation of materials.
Radar and sonar are examples of inverse scattering methods that are
used routinely nowadays. In this case we consider the inverse problem
of determining the nonlinearity for  critical semilinear wave
equations. This is joint work with A, Sa Barreto and Y. Wang.

Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Claudio Muñoz

 

Multiplicidad de soluciones por cambios de magnitud

Speaker: Pilar Herreros

Pontificia Universidad Católica de Chile

Date: Tuesday, October 4, 2022 at 12 Santiago time

Abstract: Estudiaremos las soluciones radialmente simétricas del problema $$ \Delta u+f(u)=0,\quad x\in \mathbb{R}^N, N> 2,   \lim_{|x|\to \infty} u(x)=0. $$ Veremos que podemos generar nuevas soluciones del problema si introducimos cambios bruscos en la magnitud de la función f. Usando esto construiremos funciones f, definidas por partes, tales que el problema tiene cualquier número pre-determinado de soluciones.

Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Gabrielle Nornberg

Time periodic solutions for 3D quasi-geostrophic model

Speaker: Claudia García

Universitat de Barcelona, Spain

Date: Tuesday, September 27, 2022 at 12 Santiago time

Abstract: The aim of this talk is to study time periodic solutions for 3D inviscid quasigeostrophic model. We show the existence of non trivial simply-connected rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the vertical axis. The construction of those special solutions are done through bifurcation theory. In general, the spectral problem is very delicate and strongly depends on the shape of the initial stationary solutions. More specifically, the spectral study can be related to an eigenvalue problem of a self-adjoint compact operator and we are able to implement the bifurcation only from the largest eigenvalues of such operator which are simple. At the end of the talk, we will speak also about the doubly-connected case. This is a joint work with T. Hmidi and J. Mateu.

Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Claudio Muñoz

Long-time behavior of a sexual reproduction model under the effect of strongly convex selection

Speaker: David Poyato

University of Granada, Spain

Date: Tuesday, September 20, 2022 at 12 Santiago time

Abstract: The Fisher infinitesimal model is a widely used statistical model in quantitative genetics that describes the propagation of a quantitative trait along generations of a population subjected to sexual reproduction. Recently, this model has pulled the attention of the mathematical community and some integro-differential equations have been proposed to study the precise dynamics of traits under the coupled effect of sexual reproduction and natural selection. Whilst some partial results have already been obtained, the complete understanding of the long-time behavior is essentially unknown when selection is not necessarily weak. In this talk, I will introduce a simplified time-discrete version inspired in the previous time-continuous models, and I will present two novel results on the long-time behavior of solutions to such a model. First, when selection has quadratic shape, we find quantitative convergence rates toward a unique equilibrium for generic initial data. Second, when selection is any strongly convex function, we recover similar convergence rates toward a locally-unique equilibrium for initial data sufficiently close to such an equilibrium. Our method of proof relies on a novel Caffarelli-type maximum principle for the Monge-Ampère equation, which provides a sharp contraction factor on a L^\infty version of the Fisher information. This is a joint work with Vincent Calvez, Filippo Santambrogio and Thomas Lepoutre.

Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Claudio Muñoz

Sobre ecuaciones, geometría discreta y distorsión

Speaker: Rodolfo Viera 

Pontificia Universidad Católica de Chile

Date: Tuesday, September 6, 2022 at 12 Santiago time

Abstract: En 1994, Gromov preguntó si toda red separada del plano \( X\subset\mathbb{R}^2 \) (i.e, un conjunto discreto y denso de una manera uniforme) es bi-Lipschitz equivalente al lattice est\’andar \(\mathbb{Z}^2 \) (i.e si X es bi-Lipschitz rectificable). Esto fue respondido de manera negativa por Burago y Kleiner, e independientemente por McMullen. Su demostración se basa en la existencia de una función de densidad \(\rho:[0,1]^2\to\mathbb{R}\) tal que \( 0<\inf\rho<\sup\rho<\infty \) y para la cual la ecuación

$$
Jac(f)=\rho\qquad a.e
$$

no tiene solución bi-Lipschitz \( f:[0,1]^2\to\mathbb{R}^2\). En esta charla veremos algunos resultados en esta línea, por ejemplo condiciones suficientes para asegurar la rectificabilidad de una red separada como consecuencia de la existencia de soluciones bi-Lipschitz para ciertas ecuaciones que involucran un jacobiano. También intentaremos pasar por otros resultados de no-rectificabilidad bajo condiciones más débiles que bi-Lipchitz.

Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Hanne Van Den Bosch

 

YouTube video (in Spanish)