Networks, BPS states counting, and exact WKB

Seminar: 
Clusters and Geometry
Event time: 
Friday, April 23, 2021 - 1:00pm
Speaker: 
Fei Yan
Speaker affiliation: 
Rutgers University
Event description: 

In this talk I will describe the construction of a link "invariant" (with possible wall-crossing behavior) for links L in a 3-manifold M, where M is a Riemann surface C times a real line. This construction computes familiar link invariant in a new way, moreover it unifies that computation with the computation of framed BPS indices counting ground states with spin for line defects in 4d N=2 theories of class-S. Certain networks on C play an important role in the construction. I will also mention possible extensions to general 3-manifolds M admitting tetrahedron triangulations, as well as connections to the exact WKB method in the study of Schroedinger-like equations.