Symplectic leaves and representation theory

Given a complex algebraic variety with a Poisson structure, one can ask for its decomposition into symplectic leaves: the foliation by flows of Hamiltonian vector fields.  Although a priori not guaranteed, in many situations these strata are themselves algebraic varieties, and recover previously-studied stratifications.  In this talk I will overview aspects of this theory, before discussing joint work related to representation theory: stratifications of Coulomb branches for quiver gauge theories.

Alex Weekes obtained his PhD from the University of Toronto in 2016, and subsequently held postdoc fellowships at the Perimeter Institute from 2016-2019 and at the University of British Columbia from 2019-2021.  Since leaving UBC, Alex joined the Department of Mathematics & Statistics at the University of Saskatchewan as an assistant professor.