University of Massachusetts, Amherst • July 8, 2017

8:30am–9:25am

Registration

9:25am

Welcoming remarks

9:30am–10:30am

Erik Carlsson

(UC Davis)

(UC Davis)

I will explain the construction of the algebra introduced recently by Anton Mellit and myself in our proof of the shuffle conjecture, which has many elements in common with DAHA's, and has recently been finding applications to knot invariants. I will then describe a current project with Eugene Gorsky and Mellit, in which we have discovered a geometric description of this algebra via the torus-equivariant K-theory of a certain smooth subscheme of the flag Hilbert scheme, which parametrizes flags of ideals of finite codimension in

10:30am

Coffee break

11:00am–12:00pm

Matthew Hogencamp (USC)

I will discuss a technique, introduced in joint work with Ben Elias, for computing triply graded Khovanov-Rozansky homology. Using this technique, Anton Mellit recently computed the homology of all positive torus knots, extending earlier work of myself and Elias.

12:00pm–2:00pm

Lunch

2:00pm–3:00pm

Lev Rozansky (UNC)

This is a joint work with A. Oblomkov. First, I will explain how we use two categories of equivariant matrix factorizations in order to categorify ordinary and affine Hecke algebras and Ocneanu trace. Second, I will explain that these are categories of endomorphisms of special objects within 2-categories related to the commuting variety and to the Hilbert scheme of points on

3:00pm–4:00pm

Paul Wedrich

(Imperial College London)

(Imperial College London)

Khovanov-Rozansky link homologies can be extended to give functorial invariants of links in thickened surfaces, which categorify the evaluation of links in type A skein algebras. An interesting question is whether such link homology functors can be made monoidal, so as to categorify the skein algebra multiplication as well. Evidence that (and hints on how) this should be possible exists in the form of certain positivity phenomena in skein algebras. I will talk about this story and report on work in progress with Hoel Queffelec that aims towards categorifying the gl(2) skein algebra of the torus.

4:00pm

Coffee break

4:30pm–5:30pm

Anton Mellit

(IST Austria)

(IST Austria)

I will study knot invariants which arise naturally from convolutions of sheaves on GL

Coming soon.