# Twisted matrix factorizations and loop groups

 Members' Seminar Topic: Twisted matrix factorizations and loop groups Speaker: Daniel Freed Affiliation: University of Texas, Austin; Member, School of Mathematics and Natural Sciences Date: Monday, February 9 Time/Room: 2:00pm - 3:00pm/S-101 Video Link: http://video.ias.edu/membersem/2015/0209-DanielFreed

The data of a compact Lie group $G$ and a degree 4 cohomology class on its classifying space leads to invariants in low-dimensional topology as well as important representations of the infinite dimensional group of loops in $G$. Previous work with Mike Hopkins and Constantin Teleman brought the twisted equivariant topological K-theory of $G$ into the game, but only on the level of equivalence classes. After reviewing these ideas I will describe ongoing work with Teleman which gives a geometric construction of the representation categories.