Noticias en español
Neural Implicit Surface Evolution using Differential Equations.
Abstract: In this talk, we present a machine learning framework that uses smooth neural networks to model dynamic variations of implicit surfaces under partial differential equations. Examples include evolving an initial surface towards vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of implicit surfaces regularized by specific differential equations.
Read MoreCosmología Primordial.
Abstract: Nuestro entendimiento del origen del universo ha cambiado dramáticamente durante los últimos 40 años. Hoy sabemos que la estructura de gran escala del universo (compuesto por galaxias) debe su existencia a pequeñas fluctuaciones del espacio y el tiempo -fluctuaciones primordiales- ya presentes durante el Big-Bang. La teoría más aceptada para explicar el origen de estas fluctuaciones sostiene que ellas se deben a procesos cuánticos ocurridos antes del Big-Bang, durante una época conocida como inflación cósmica. Este cuadro lo hemos forjado utilizando observaciones basadas en...
Read MoreExistence of solutions on the critical hyperbola for a pure Lane-Emden system with Neumann boundary conditions.
Abstract: I will present some recent results obtained in collaboration with A. Pistoia and H. Tavares for a Lane-Emden system on a bounded regular domain with Neumann boundary conditions and critical nonlinearities. We show that, under suitable conditions on the exponents in the nonlinearities, least-energy (sign-changing) solutions exist. In the proof we exploit a dual variational formulation which allows to deal with the strong indefinite character of the problem, and we establish a compactness condition which is based on a new Cherrier type inequality. We then prove such condition by...
Read MoreNon-existence results for an eigenvalue problem involving Lipschitzian nonlinearities with non-positive primitive and applications.
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Read MoreNonlocal Aggregation-Difusion Equations: entropies, gradient flows, phase transitions and applications.
Abstract: his talk will be devoted to an overview of recent results understanding the bifurcation analysis of nonlinear Fokker-Planck equations arising in a myriad of applications such as consensus formation, optimization, granular media, swarming behavior, opinion dynamics and nancial mathematics to name a few. We will present several results related to localized Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear difusion Keller-Segel type models in several settings. We will show the existence of continuous or discontinuous phase transitions on the torus under...
Read MoreOn Space-Time Formulations and Boundary Integral Equations for the Wave Equation.
Abstract: Space-time discretization methods are becoming increasingly popular, since they allow adaptivity in space and time simultaneously, and can use parallel iterative solution strategies for time-dependent problems. However, in order to exploit these advantages, one needs to have a complete numerical analysis of the corresponding Galerkin methods. In this talk, we consider the wave equation with on a Lipschitz bounded domain, with either Dirichlet or Neumann boundary conditions, and with zero initial conditions. The first step to build the required numerical analysis was to show new...
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