Mini-course ‘ Nonlinear Markov semigroups and processes with applications to statistical mechanics, evolutionary biology and control theory ’

On October 17-26 a mini-course ‘Nonlinear Markov semigroups and processes with applications to statistical mechanics, evolutionary biology and control theory’ by Vassili Kolokoltsov, Professor of University of Warwick (UK) will be delivered at HSE. The event is organized by the Laboratory of Stochastic Analysis and its Applications.

Abstract:

Nonlinear Markov semigroups are the nonlinear semigroups of mapping on the space of probability measures. This  notion extends naturally the notion of usual (linear) Markov semigroups. Similarly, as linear spaces can be considered as tangent spaces to nonlinear manifolds, usual Markov processes can be considered as tangent to nonlinear Markov processes.  Though nonlinear processes are met everywhere in natural science, economics and natural science, their systematic study was initiated quite recently. Special aspect of the most recent developments is connected with the control theory of nonlinear processes (nonlinear Markov games and mean-field games).  In the course we develop the basic theory starting from the simplest models. All results will be illustrated on the concrete  applications to physics (Equation of Boltzmann, Vlasov, Smoluchovskii, Landau, McKean diffusion, nonlinear Schroedinger equation, etc), evolutionary biology (replicator dynamics) and control theory (mean-field games).

Schedule

17 October - 18:00 - 21:00 room 2219
19 October - 18:00 - 21:00 room 2220
20 October - 18:00 - 21:00 room 2220
24 October - 18:00 - 21:00 room 2220
26 October - 18:00 - 21:00 room 2220

Location: Moscow, 26 Shabolovka st., room:2220, 2219

Working language is English

Course is open to anyone interested. Whether you need the pass to the Higher School of Economics, do not hesitate to contact the lab manager Julia Pavlyuk ypavlyuk@hse.ru