Illia Koval (Insitute of Science and Technology, Austria):

Title: Mushroom KAM theory

Abstract: In classical KAM theory, a certain nondegeneracy of the Hessian of the unperturbed  Hamiltonian is crucial 
to show the existence of invariant tori. These invariant tori have to be the graphs of Lipschitz functions. However, 
when such a type of nondegeneracy is violated, very little is known. Inspired by some numerical examples of Simó, we will 
show the existence of mushroom-shaped non-graph meandering invariant tori and that they are generic. 
This is a joint work in progress with Vadim Kaloshin and Yi Pan.