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Mini-course in Pathwise integration and particle methods

Date: 18 to 21 April 2016 (exact schedule TBA)

Venue: International Centre for Mathematical Sciences (ICMS) 

This mini-course brings to Edinburgh experts in two exciting strands of mathematics. The first, on pathwise integration which relates heavily to the recent Fields Medal attributed to Hairer and with strong links to Physics and Finance. The second one relates to the field of McKean-Vlasov type equations. These equations provide a probabilistic tool to study many nonlinear PDEs  (Burgers Equations, Navier-Stokes Equations) and recently has been proved to be extremely useful in the study of classical solutions of the Master Equations that arise in the theory of  Mean Field Games by J.-M. Lasry and P. Lions. The choice of both topics was made keeping research interests at UoE, Heriot-Watt University (HW) and to students of the Maxwell's Institute Graduate School in Analysis and its Applications (MIGSAA). Both topics bridge probability and analysis and have a broad range of action, from finance to particle physics. The mini-courses and added talks will expose the members of the Mathematical community (UoE, HW and Maxwell Institute) and the young MIGSAA students to cutting-edge research, as well as strengthen Edinburgh’s links to two of the strongest research groups in Europe (Berlin and Paris). 

The core of the event are the mini-courses. Nonetheless, we aim at enriching the event with several talks from Ph.D. students and staff members of the Maxwell Institute (UoE & HW). Peter Imkeller has kindly agreed to give a mini-course of 6 to 10 hours depending on organizational restrictions on “A Fourier Based Approach of (Stochastic) Integration; Applications to Pathwise SPDE”.  The second mini-course, on “Analysis and Simulations of McKean-Vlasov equations”, will be delivered by Mireille Bossy (Sophia Antipolis - Inria, Paris). Both speakers are confirmed.

P. Imkeller is a world-class researcher in the field of probability and stochastics with substantial contributions in Malliavin calculus, Backward Stochastic Differential Equations, Stochastic Partial Differential Equations, meta-stability developments in paleoclimate models and others. More recently he has co-authored with M. Gubinelli (Paris-Dauphine) and N. Perkowski (Humboldt University) an extremely visible work on pathwise integration using tools from both analysis and probability. This work has strong links to Hairer’s regularity structures theory and “para-controlled distributions”.

M. Bossy, is a world-class researcher in the field of probability and stochastics with strong contributions in Stochastic Particle Systems, Probabilistic methods for fully non-linear PDEs. She has made a very significant contribution to the theory of singular McKean-Vlasov equations that for example arise in Lagrangian approach to Fluid mechanics.  The theory of mean-field interacting particle systems was pioneered by the work of H. McKean, where he gave a probabilistic interpretation of a class of nonlinear PDEs arising in fluid dynamics. For example, stochastic particles model; physical particles in fluid dynamics; behavior of interacting agents in economics or social networks, interacting neurons in biology. Therefore, the study of the system and its limiting behavior has strong implications for many fields and is of great importance in the international arena of applied probability, numerical analysis, and statistics.

We hope to see you there!

Goncalo dos Reis and Lukasz Szpruch

and please link the names to our personal websites

http://www.maths.ed.ac.uk/~gdosrei

http://www.maths.ed.ac.uk/~lszpruch

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