Fokker-Planck equations

Illustration weak approximation SDE

AMCS 336 Numerical Methods for Stochastic Differential Equations with connections to Machine Learning

stochastic differential equations Ito integral Monte Carlo Multilevel Monte Carlo Importance sampling Variance Reduction Kolmogorov Backward Equation Fokker-Planck equations Hamilton-Jabobi-Bellman Stochastic Optimal Control

The goal of this course is to give basic knowledge of stochastic differential equations and their numerical solution, useful for scientific and engineering modeling, guided by some problems in applications in financial mathematics, material science, geophysical flow problems, turbulent diffusion, control theory, and Monte Carlo methods.

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.