Classical Integrable Systems on Stratified Symplectic Spaces

Explore the mathematical foundations of classical integrable systems within the framework of stratified symplectic spaces in this hour-long conference talk delivered at ICBS2025. Delve into the intricate relationships between symplectic geometry and integrable systems, examining how classical mechanical systems can be analyzed on spaces with stratified structures. Learn about the theoretical underpinnings that connect symplectic manifolds with singular or stratified geometries to the study of completely integrable Hamiltonian systems. Discover advanced mathematical concepts including the geometric properties of stratified spaces, symplectic reduction techniques, and their applications to understanding the behavior of integrable dynamical systems. Gain insights into current research developments in mathematical physics where symplectic geometry meets integrability theory, particularly focusing on systems that exhibit both classical integrability and geometric complexity through stratification.