Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Symplectic implosion was developed to solve the problem that the symplectic cross-section of a Hamiltonian $K$-space is usually not symplectic, when $K$ is a compact Lie group. The symplectic implosion is a stratified symplectic space, introduced in a 2002 paper of the speaker with Guillemin and Sjamaar. I survey some examples showing how symplectic implosion has been used. I describe the universal imploded cross-section, which is the imploded cross-section of the cotangent bundle of a compact Lie group. Imploded cross-sections are normally not smooth manifolds. We describe some invariants (for example intersection homology) which replace homology for singular stratified spaces. (Joint work with Sina Zabanfahm)