Algebra and Algebraic Geometry Seminar - Jeremy Lane - Integrable systems and action-angle coordinates from algebraic geometry and representation theory
Title: Integrable systems and action-angle coordinates from algebraic geometry and representation theory
Abstract: We construct integrable systems with global action-angle coordinates on an arbitrary multiplicity-free convex Hamiltonian K-manifolds, for an arbitrary compact connected Lie group K. Our construction derives in a natural way from earlier ideas and results in representation theory (canonical bases) and algebraic geometry (toric degenerations). The key is a magical tool -- the gradient-Hamiltonian vector field -- which allows us to relate toric degenerations (complex geometry) to integrable systems (symplectic geometry) with the help of a dash of Kahler geometry.
Based on joint work with Benjamin Hoffman. arXiv:2008.13656
Location: Hamilton Hall 104