New Trends in Nonlinear Diffusion: a Bridge between PDEs, Analysis and Geometry (21w5127)

Organizers

(Universidad Autónoma de Madrid)

Pedro Aceves Sánchez (North Carolina State University)

(Politecnico di Milano)

Bruno Volzone (Università di Napoli "Parthenope")

Description

The Casa Matemática Oaxaca (CMO) will host the "New Trends in Nonlinear Diffusion: a Bridge between PDEs, Analysis and Geometry" workshop in Oaxaca, from September 5 to September 10, 2021.


Diffusion processes appear in a large variety of phenomena in physical, life and economic sciences; for instance, pollution in water and air, melting of ice, stock market bubbles, spread of diseases, tumor growth, migration of populations etc. For these reasons, diffusion has constantly been an object of deep mathematical studies, which gave rise to important results in the applied sciences. One of the most used equations to describe such phenomena is the heat equation. The latter offers a very simple way to account for diffusion, hence more elaborated models have been proposed to highlight sophisticated aspects appearing in the observed phenomena, such as the porous medium, the p-Laplacian, and the anomalous (e.g. fractional) diffusion equation. Again, the heat equation possesses a very rich mathematical structure, since it can be seen at the microscopic level as a Brownian motion, at the mesoscopic level as a kinetic transport equation and it can also be recast as a gradient flow of the Gibbs-Boltzmann entropy, i.e. the steepest ascent or descent over the entropy/energy landscape with respect to an appropriate notion of distance. In particular, this last interpretation has been extremely useful for the investigation of more general diffusion-like phenomena, such as nonlinear and degenerate/singular diffusion, not only to understand the abstract geometric framework of the nonlinear equations, but also to create, for instance, unexpected and exciting correlations among different branches of Mathematics such as Optimal Transport Theory, Geometric Flows and Stochastic Analysis. An impressive record of outstanding results, which also made use of the above techniques, has been obtained in both the theory and the applications of nonlocal-nonlinear diffusion equations of several types.

In this workshop our aim is to bring together well-established and early-career researchers from the areas of Analysis of PDEs, Optimal Transport Theory and Geometric Flows to report on their latest contributions and establish new collaborations. The fields of expertise of the participants are broad and will offer a great opportunity for cross-fertilization among diverse communities.


The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT