Claudio
Muñoz

Professor at Departamento de Ingeniería Matemática (DIM), Universidad de Chile. Principal Investigator of the Center for Mathematical Modeling (CMM). Chargé de Recherche CNRS (on leave). Postal Address: Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile Beauchef 851, Torre Norte, Piso 5, Santiago, Chile. 

I obtained my PhD in Mathematics in 2010 at the University of Versailles Saint-Quentin, under the advise of Yvan Martel and Frank Merle. Carlos Kenig was my postdoctoral mentor, during 2011-2013. Previously, Manuel del Pino was my undergraduate advisor at the U. of Chile. Since 2013 I am Chargé de Recherche CNRS (on leave), and since 2020 I am Full Professor at DIM-CMM.

I am interested in Nonlinear dispersive models appearing in physics and other areas of modeling and nature, in particular: collisions, well-posedness, stability and asymptotic stability of kinks, solitons and other special nonlinear patterns, integrability and blow-up, and more recently, inverse problems, synergies between PDEs and number theory problems and the mathematics of deep neural networks in PDEs. These are particular building blocks representing the main long time behavior in dispersive models. A famous conjecture in the área, closed to my interest, states that except some very particular cases, all globally well-defined solutions in dispersive models decompose in a certain finite or infinite number of nonlinear solitons plus a radiation term that behaves as a linear evolution.