Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

by László Fehér (HUN-REN Wigner RCP and SZTE Department of Theoretical Physics)

Friday 11 Jul 2025, 14:00 → 15:00 Europe/Budapest

First, we develop sufficient conditions for guaranteeing that an integrable Hamiltonian system with symmetry group K on a manifold M descends to an integrable system on a dense open subspace of the quotient Poisson space M/K and on its symplectic leaves. Then, we present applications to reductions of master systems on cotangent bundles and Heisenberg doubles of compact Lie groups and to integrable systems on moduli spaces of flat connections. In almost all examples, the term ‘integrability’ refers to degenerate integrability, alias superintegrability. The talk is based on  joint work with Maxime Fairon (Dijon).