Infinite-dimensional Symplectic Geometry - Part 2
Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube
Overview
Explore advanced mathematical concepts in this second lecture of a three-part series on infinite-dimensional symplectic geometry, focusing on degenerate integrability in the Poisson quotient of the Heisenberg double and its relationship to Ruijsenaars-Schneider type many-body systems. Delve into the reduction of integrable master systems on classical doubles of semisimple, connected, and simply connected compact Lie groups, examining how these systems are generated by class functions and invariant functions of Lie algebra in the cotangent bundle case. Learn about the quotient space of the internally fused double and its representation of flat principal G-connections on the torus with a hole, while understanding how degenerate integrability persists in the smooth component of the Poisson quotient. Master explicit formulas for reduced Poisson structure and equations of motion through dynamical r-matrices, with particular emphasis on the interpretation of reduced systems as Ruijsenaars-Schneider type many-body systems extended by spin degrees of freedom.
Syllabus
Tobias Diez - Infinite-dimensional Symplectic Geometry, Part 2
Taught by
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)