#### Chandrasekhar Hall

#### Deformations of the Hitchin Integrable System and Supersymmetric Quantum Field Theories

#### Aswin Balasubramanian

##### Rutgers University

*I will begin by reviewing the relationship between Hitchin's Integrable System and 4d N=2 Supersymmetric Quantum Field Theories. I will then discuss two classes of deformations of the Hitchin system which correspond, in the physical context, to relevant and marginal deformations of a conformal theory. The study of relevant deformations turns out to be related to the theory of sheets in a complex Lie algebra and their classification leads to a surprising duality between sheets in a Lie algebra and Slodowy slices in the Langlands dual Lie algebra (work done with J. Distler) . I will also discuss marginal deformations which are related to studying the Hitchin system as a family over the moduli space of curves including over nodal curves (ongoing project with J. Distler and R. Donagi).*

Done