Calculus of Variations and Geometric Measure Theory

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

created by mari1 on 30 Aug 2021

5 sep 2021 - 10 sep 2021   [open in google calendar]

Oaxaca (CMO), Mexico (Online)

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 entropyenergy 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 degeneratesingular 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.

Organizers: Pedro Aceves-anchez, Matteo Bonforte, Matteo Muratori, Bruno Volzone.

Speakers: Goro Akagi, Anton Arnold, Elvise Berchio, José Antonio Carrillo, Gilles Carron, Michele Coti Zelati, Katy Craig, Azahara De la Torre, Manuel Del Pino, Felix del Teso, Jean Dolbeaut, Vincenzo Ferone, Alessio Figalli, Maria del Mar González, Gabriele Grillo, Maria Gualdiani, Mikaela Iacobelli, Mihaela Ignatova, Kazuhiro Ishige, Tatsuki Kawakami, Michael Loss, Edoardo Mainini, Luciano Mari, Monica Musso, Bruno Nazaret, Shin-Ichi Ohta, Ramon Plaza, Fabio Punzo, Fernando Quirós, Xavier Ros-Oton, Christian Schmeiser, Luis Silvestre, Nikita Simonov, Yannick Sire, Diana Stan, Asuka Takatsu, Alexis Vasseur, Juan Luis Vazquez, Yao Yao.