NBMPS 60 Dimofte

Tudor DIMOFTE (University of Edinburgh)

Title: Categorifying the Schur Index

Abstract: The Schur index of a 4d N=2 theory counts local operators in the cohomology of a particular supercharge Q. In superconformal theories, it was shown to coincide with the character of an associated VOA. I will discuss some current work with Wenjun Niu that goes in a (literally) orthogonal direction, explaining how local operators in Q-cohomology arise from a geometric description of the category of line operators in 4d N=2 theories (due to Kapustin and Cautis-Williams), and how this idea generalizes to operators at junctions of Wilson-'t Hooft lines, bound to surface defects, and in the presence of boundary conditions (half-indices). Mathematically, derived algebraic geometry plays a key role throughout.