Keller-Segel-type models

Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications

Prof. Jose Carrillo, Department of Mathematics, University of Oxford, UK

Jan 10, 15:30 - 17:00

B2 L5 R5209

Fokker-Planck equations Cucker-Smale orientation dynamics McKean-Vlasov equations Keller-Segel-type models

This talk will be devoted to an overview of recent results in understanding the bifurcation analysis of nonlinear Fokker-Planck equations arising in a myriad of applications such as consensus formation, optimization, granular media, swarming behavior, opinion dynamics, and financial mathematics to name a few. We will present several results related to localized Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear diffusion Keller-Segel-type models in several settings. We will show the existence of continuous or discontinuous phase transitions on the torus under suitable assumptions on the Fourier modes of the interaction potential.