video of the talk

I’ve frequently heard the assertion that “hyperkahler manifolds are self-mirror up to rotation.” I’m not so sure this is true in general, but I know one example of such a variety:  multiplicative hypertoric varieties; these are what happens when you cut up a real torus into polytopes, and then send the polytopes to have a toric hyperkahler party.  I’ll discuss recent work with Gammage and McBreen showing that self-homological homological mirror symmetry after rotation...

video of the talk 

Abstract: One key tool in understanding categories of representations of Lie (super)algebras and quantum groups is how the fun tour of tensor product with finite dimensional representations behaves.  I’ll first explain how my work as well as that of many others has led to a good understanding of this in the type A case, and then say a few words about how we might generalize to BCD types.

video of the talk

One of the central topics of the interaction between QFT and math is mirror symmetry for 2d theories. This theory has a more mysterious and exotic friend one dimension higher, sometimes called 3d mirror symmetry, which relates two 3-dimensional theories with N=4 supersymmetry. For roughly a decade, I struggled to understand this phenomenon without understanding what most of the words in the previous sentence meant. Eventually, I wised up and based on work of Braverman, Finkelberg, Nakajima, Dimofte,...

video of the talk

Abstract: 

Work on Bezrukavnikov and Kaledin provides a bridge between representation theory and algebraic geometry, giving an equivalence of derived categories between certain categories of coherent sheaves and non-commutative algebras. Their original construction involved a strange detour into the land of characteristic p, but with some insight from 3-d gauge theory, we can avoid this in the case of BFN Coulomb branches,...