|October 21, 2014|
Program on Partial Differential Equations
The Fields Institute Coxeter Lecture Series (CLS) brings a leading mathematician to the Institute to give a series of three lectures in the field of the current thematic program.The first talk is an overview for a general mathematical audience, postdoctoral fellows and graduate students. The other two talks are chosen, in collaboration with the organizers of the thematic program, to target specialists in the field.
Sergei Kuksin is a leading mathematician in the field of Hamiltonian partial differential equations and infinite dimensional dynamical systems. He has been in the forefront of the study of invariant structures in the phase space of Hamiltonian PDEs and of their behaviour under perturbation. This work exploits the infinite dimensional Hamiltonian systems perspective on evolution PDEs, and involves the development of detailed analytic techniques and their extensions from the finite dimensional setting of classical Hamiltonian mechanics. His work includes as well results on infinite dimensional KAM theory, as well as Nekhoroshev theory and Arnold diffusion. He has written over 50 influential research papers, and is the author of a recent monograph Analysis of Hamiltonian PDEs, published by the Oxford Press.
One of his current interests is the stochastic behaviour of Navier-Stokes equations, including central questions on the uniqueness of invariant Gibbs measures on the space of divergence-free vector fields. His mathematical interests also include plasticity, integrable partial differential equations, averaging theory, turbulence in nonlinear PDEs, and elliptic equations for maps valued in compact manifolds.
Professor Kuksin is a fellow of the Royal Society of Edinburgh.