Hans Jockers:Remarks on Modularity in Quantum K-Theory

Abstract: In this talk we present some observations about the modular properties of 3d BPS half-indices of particular N=2 3d gauge theories. These indices connect to quantum K-theory via the 3d gauge theory quantum K-theory correspondence. They are solutions to certain q-difference equations, which — for particular classes of N=2 3d gauge theories — relate to the theory of bilateral q-series and modular q-characters of two dimensional conformal field theories in a certain massless limit.