Talk page
Title:
BPS states and the Hitchin equations
Speaker:
Abstract:
I will describe a conjectured connection between physics and geometry. The relevant physics is supersymmetric quantum field theory in four dimensions. The relevant geometry is a system of partial differential equations in two dimensions, the "Hitchin equations". These two things at first look like they have nothing to do with each other, but over the last decade it has been appreciated that they are actually closely connected, with the surprising link between them provided by some integers known as "BPS state counts" or "Donaldson-Thomas invariants." My aim is to explain some aspects of this conjectural picture, and some recent progress toward proving that it is actually correct. The original proposal appears in my joint work with Gaiotto-Moore, and more recent progress involves work of Mazzeo-Swoboda-Weiss-Witt, my joint work with Dumas, and work of Fredrickson.
Link:
Workshop: