Applied Maths Seminar: Feher -- Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

Laszlo Feher (The University of Szeged) is visiting us until 26 September and will give
a seminar on Wednesday 10 September at 1pm in Carslaw 275.  Carslaw 275 is our location
for the rest of semester.  

Title: Integrable systems from Poisson reductions of generalized Hamiltonian torus
actions 

Abstract: We develop a set of sufficient conditions for guaranteeing that an integrable
system with symmetry group K on a Poisson manifold M descends to an integrable system on
a dense open subspace of the quotient Poisson space M/K and on its symplectic leaves.
We shall focus on the simplest examples given by reductions of `master systems' on
cotangent bundles of compact Lie groups.  Time permitting, we shall also deal with
applications associated with Heisenberg doubles and with moduli spaces of flat
connections.  In almost all examples, the term `integrability’ refers to degenerate
integrability, alias superintegrability.  

The talk is aimed to be self-contained in the sense that all necessary notions will be
defined.  Details and references can be found in the recent preprint arXiv:2507.12051
based on collaboration with Maxime Fairon (Dijon).