Informal Mathematical Physics Seminar

organized by Igor Krichever and Andrei Okounkov

Mondays, 5:00, Room 507

Schedule of talks for Fall 2012:


September 10
Michael McBreen and Daniel Shenfeld
Hypertoric varieties and
abelianization in quantum cohomology
September 17 Alexander Veselov Universality in Lie algebras and Chern-Simons theory
September 24
Michael McBreen and Daniel Shenfeld continuing
October 1
Yuri Suris
Hirota-Kimura discretization of integrable systems and addition theorems
October 8
Daniel Shenfeld
continuing
October 15 Hiraku Nakajima
October 22
Michael McBreen

Nov 12
Eugene Gorsky
Cherednik algebras and Khovanov-Rozansky homology
Nov 19
Balazs Szendroi
Geometric engineering and refined DT theory


Abstracts

Alexander Veselov, Loughborough University, UK

Title: "Universality in Lie algebras and Chern-Simons theory"

Abstract. I will show that the eigenvalues of certain natural Casimir
operators in the adjoint representation of simple Lie algebras can be
expressed rationally in the universal Vogel parameters and give explicit
formulae for the corresponding generating functions. Similar universal
formulae can be given for some quantities in Chern-Simons theory on a 3D
sphere. The talk is based on joint results with Mkrtchyan and Sergeev.

Yuri Suris, Technische Universit├Ąt Berlin

Title. "Hirota-Kimura discretization of integrable systems and addition theorems"

Abstract: "Hirota-Kimura discretization method is applicable to any integrable system with quadratic vector field and leads to birational maps which very often turn out to be integrable, as well. In this talk, we are going to present an overview of available results on this discretization method and discuss its relations with addition theorems for elliptic and more general abelian functions"

Eugene Gorsky, Simons Center for Geometry and Physics

Cherednik algebras and Khovanov-Rozansky homology

I will describe a model for the HOMFLY homology of the (m,n) torus knot
using the finite-dimensional irreducible representation L_{m/n} of the rational Cherednik
algebra with parameter m/n. The m-n symmetry of this construction and connections to the
q,t-Catalan numbers of A. Garsia and M. Haiman will be also discussed. The talk is based
on a joint work with A.Oblomkov, J. Rasmussen and V. Shende.