Abstract: In this talk we will analyze the existence and the structure of different sign-changing solutions to the Yamabe equation in the whole space and we will use them to find positive solutions to critical competitive systems in dimension 4.
Venue: Online via Zoom / Sala de seminarios DIM, 5th floor, Beauchef 851
Chair: Claudio Muñoz
YouTube video (in Spanish)
Abstract: El Sistema de Vlasov-Poisson Plano es usado para modelar objetos astronómicos extremadamente planos, a través de la evolución de una distribución de partículas en el plano de fase, las cuales autointeractúan a través del campo gravitacional inducido por ellas mismas.
En este trabajo se estudia la construcción de estados estacionarios del Sistema de Vlasov-Poisson Plano en presencia de un potencial gravitacional externo, inducido por una densidad de masa fija. La construcción de dichos estados se realiza a través de la minimización de los funcionales de Energía-Casimir, los cuales permiten probar resultados de estabilidad no lineal para dichos estados estacionarios.
Venue: Online via Zoom / Sala multimedia CMM, 6th floor, Beauchef 851
Chair: Paola Rioseco
YouTube video (in Spanish)
Abstract: Our recently acquired ability to detect gravitational waves has expanded our senses and our possibilities of inquiring about the Universe. As a new era of gravitational wave detections rapidly unfolds, the importance of having accurate models for their signals becomes increasingly important. In this context, we will discuss numerical simulations of black hole binaries. In particular, we will focus on how they are made, what they help us achieve, and what are the current challenges in this research area.
Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Paola Rioseco
YouTube video (in Spanish)
Abstract: In this talk we will discuss some problems related to the notion of Fourier interpolation: formulas where one can recover functions from its values over a certain discrete set, and the values of its Fourier transform over a dual discrete set. These formulas arrive naturally in many situations, and we will mention a few related to certain kinds of uncertainty principles, and the theory of sphere packing.
Chair: Rayssa Caju
Abstract: In joint work with F. Pacella, we study the existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci’s extremal operators in dimension two and higher. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover, for the (negative) Pucci P^- operator, we show the existence of a critical exponent and give bounds for it. The same technique is then applied in higher dimensions to improve the previously known bounds.
Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Gabrielle Nornberg
Abstract: In this talk, we consider the Dirichlet problem for the scalar-field equation in a large annulus in the three-dimensional sphere. We obtain the existence, uniqueness, and multiplicity results of the positive solutions depending only on the latitude. This is joint work with Noaki Shioji (Yokohama National University) and Kohtaro Watanabe (National Defense Academy).
Venue: Online via Zoom / Sala de seminarios John Von Neumann, 7th floor, Beauchef 851
Chair: Hanne Van Den Bosch
YouTube video (in English)
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
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
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
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
YouTube video (in Spanish)