### September 9, 2019

TITLE: Hasse diagrams for symplectic singularities

ABSTRACT: Symplectic singularities appear in physics as the so called Higgs branches and Coulomb branches of supersymmetric gauge theories. They naturally form a structure of symplectic leaves with a partial order that can be depicted by a Hasse diagram.

The physical interpretation of this geometric structure is the so called “partial Higgs mechanism” where, on each leaf, the so-called “unbroken gauge group” is fixed. Simple examples of such symplectic singularities are closures of nilpotent orbits, and each leaf is associated with a smaller nilpotent orbit.

In this talk, we will explain these points, present the physical intuition, and suggest some results for Hasse diagrams of various Higgs branches that are of interest in some physical systems that arise in string theory.