# SIMBa: Supercritical diffusion: memes, stonks and more

El proper dimecres, 20 d’octubre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Damià Torres Latorre
Universitat: Universitat de Barcelona

Data: Wednesday, October 20th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Supercritical diffusion: memes, stonks and more
Resum: In this talk, I will explain the foundations of the theory of elliptic nonlocal PDE, focusing on the fractional Laplacian, $(-\Delta)^{s}$ a model example, and then some recent results on the supercritical fractional obstacle problem.

The first part will start with the relation of fractional operators to jump-diffusion (Lévy) processes and some physical applications. Then, I will give an overview of the basic properties of solutions and compare them to harmonic functions, and also comment on the Caffarelli-Silvestre extension.

In the second part, I will give an idea of how stock prices can be modelled with a nonlocal parabolic obstacle problem, compare the scaling properties of the problem depending on the value of sand present the main points of a recent work with X. Ros-Oton where we study the regularity of the solutions in the supercritical case.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a `seminari(dot)simba(at)ub(dot)edu`.