Colloquim Mathematics - Nikolay Martynchuk, University of Groningen

Title: First steps in the topology of integrable Hamiltonian systems

Abstract:

In this talk, we shall give an overview of the topological theory of integrable systems, starting with the classical notion of monodromy introduced by Duistermaat and the marked molecules of Fomenko and Zieschang. Afterwards, we will move to the more recent developments around integrable systems with a scattering dynamics and show how the classical topological invariants generalise to this context. Time-permitting, a connection to symplectic geometry, through the example of an A_2 singularity, will also be discussed. The talk is based on joint works with K. Efstathiou, H. Waalkens, H. Dullin, and E. Kudryavtseva.