MS Seminar (Mathematics - String Theory)

Speaker: Harold Williams (U Texas at Austin )
Title: Relativistic Integrable Systems, Quiver Representations, and Line Operators
Date: Tue, Sep 16, 2014, 13:15 - 14:45
Place: Seminar Room A
Abstract: We describe some new connections between integrable systems, specifically relativistic or cluster integrable systems, and the representation theory of quivers with potential. These integrable systems turn out to admit a kind of categorification wherein their Hamiltonians are identified with generating functions of Euler characteristics of quiver Grassmannians, and their integrability can be reinterpreted as a consequence of the special properties of certain quiver representations. From a different point of view, these results are aimed at making mathematically precise various predictions coming from the theory of line operators in 4d N=2 theories of class S(in the case we focus on, Wilson loops in pure N=2 SYM). We discuss various extensions of this work still in progress, and why a better understanding of these line operators could lead to a better understanding of Lusztig's dual canonical basis and its generalizations.