Joint BCAM-UPV/EHU Data Science and Artificial Intelligence seminar: A variational approach to nonlocal interactions: discrete-to-continuum analysis, ground states and geometric evolutions.

Abstract
We consider a core-radius approach to nonlocal perimeters governed by isotropic kernels having critical and supercritical exponents, extending the nowadays classical notion of s-fractional perimeter, defined for 0 < s < 1, to the case s>1.

In the second part of the talk we introduce a model for hard spheres interacting through attractive Riesz type potentials, and we study its thermodynamic limit.

In the third part of the talk we prove that s -fractional heat flows converge to the standard heat flow as s go to 1, and to a degenerate ODE type flow as s go to 0.

More info at https://sites.google.com/view/apdebilbao/home