Mathematical Physics

This series consists of talks in the area of Mathematical Physics.

Seminar Series Events/Videos

May 30 2017 - 2:00pm
Room #: 394
Speaker(s):
Scientific Areas:
Jun 12 2017 - 2:00pm
Room #: 394
Scientific Areas:

 

Friday May 19, 2017
Speaker(s): 

I will present some results on three-dimensional gauge theory from the point of view of extended topological field theory. In this setting a theory is specified by describing its collection of boundary conditions - in our case, a collection of categories (standing in for 2d TFTs) with a prescribed symmetry group G.

Collection/Series: 
Scientific Areas: 

 

Monday May 15, 2017
Speaker(s): 

The notion of singular support for coherent sheaves was introduced by Arinkin and Gaitsgory in order to carefully state the geometric Langlands conjecture.  This is a conjectural equivalence of categories of sheaves on certain moduli spaces: in order to make the conjecture reasonable one needs to restrict to sheaves which satisfy a certain "singular support condition".  In this talk I'll explain how to think about this singular support condition from the point of view of boundary conditions in twisted N=4 gauge theory.  Specifically, Arinkin and Gaitsgory's singular su

Collection/Series: 
Scientific Areas: 

 

Thursday May 04, 2017
Speaker(s): 

In this talk, we will discuss an open Gromov-Witten invariant on hyperKahler surfaces, including K3 surfaces and certain Hitchin moduli spaces. The invariant is defined via the Lagrangian Floer theory and satisfy the Kontsevich-Soibelman wall-crossing formula and are expect to recover the generalized Donaldson-Thomas invariants studied in the work of Gaiotto-Moore-Neitzke.

Collection/Series: 
Scientific Areas: 

 

Monday May 01, 2017
Speaker(s): 

The notion of Positive Representations is a new research program devoted to the representation theory of split real quantum groups, initiated in a joint work with Igor Frenkel. It is a generalization of the special class of representations considered by J. Teschner for Uq(sl(2,R)) in Liouville theory, where it exhibits a strong parallel to the finite-dimensional representation theory of compact quantum groups, but at the same time also serves some new properties that are not available in the compact case.

Collection/Series: 
Scientific Areas: 

 

Friday Apr 28, 2017
Speaker(s): 

I will discuss some results on double loop groups that point to geometric phenomena about double affine flag varieties and double affine Grassmannian. One result of this study is a definition of double affine Kazhdan-Lusztig polynomials.

Collection/Series: 
Scientific Areas: 

 

Monday Apr 24, 2017
Speaker(s): 

This talk concerns a family of special functions common to the study of quantum conformal blocks and hypergeometric solutions to q-KZB type equations.  In the first half, I will explain two methods for their construction -- as traces of intertwining operators between representations of quantum affine algebras and as certain theta hypergeometric integrals we term Felder-Varchenko functions.  I will then explain our proof by bosonization the first case of Etingof-Varchenko's conjecture that these constructions are related by a simple renormalization.

 

Collection/Series: 
Scientific Areas: 

 

Monday Apr 10, 2017

The physics proof of the Atiyah-Singer index theorem relates the Hamiltonian and Lagrangian approaches to quantization of N=1 supersymmetric mechanics.

Collection/Series: 
Scientific Areas: 

 

Monday Mar 20, 2017
Speaker(s): 

An F-field on a manifold M is a local system of algebraically closed fields of characteristic p.  You can study local systems of vector spaces over this local system of fields.  On a 3-manifold, they are are rigid, and the rank one local systems are counted by the Alexander polynomial.  On a surface, they come in positive

Collection/Series: 
Scientific Areas: 

 

Monday Mar 13, 2017
Speaker(s): 

We define an action of the k-strand braid group on the set of cluster variables for the Grassmannian Gr(k,n), provided k divides n. The action sends clusters to clusters, preserving the underlying quivers, defining a homomorphism from the braid group to the cluster modular group for Gr(k,n). Our results can be translated to statements about clusters in Fock-Goncharov configuration spaces of affine flags, provided the number of flags is even.

Collection/Series: 
Scientific Areas: 

 

Friday Feb 24, 2017
Speaker(s): 

The Feynman diagram expansion for a Wilson loop observable in Chern-Simons gauge theory generates an infinite series of topological invariants for framed knots.  In this talk, I will describe a new perturbative formalism which conjecturally generates the same invariants for Legendrian knots in the standard contact R^3.  The formalism includes a `perturbative' localization principle which drastically simplifies the structure of calculations.  As time permits, I will provide some examples and applications.  This talk is based upon joint work with Brendan McLellan and Ruo

Collection/Series: 
Scientific Areas: 

Pages