Noticias en español
Simulations of black hole binaries and their gravitational waves.
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.
Read MoreDe soluciones de la ecuación de Yamabe que cambian de signo a soluciones positivas de sistemas críticos competitivos.
Abstract: En esta charla analizaremos la existencia y estructura de diferentes soluciones que cambian de signo de la ecuación de Yamabe y las usaremos para construir soluciones positivas de sistemas críticos de tipo competitivo en dimensión 4.
Read MoreExistence and stability of steady states of Flat Vlasov Poisson with a central mass density.
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...
Read MoreRecent developments in Fourier interpolation theory.
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.
Read MoreQualitative Properties for a class of fully nonlinear elliptic equations.
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
Read MoreExistence and multiplicity of positive solutions to the scalar-field equation on large annuli in the three-dimensional sphere.
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).
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