Event Series
Event Type
Seminar
Tuesday, January 28, 2020 1:00 PM
Sunghyuk Park (Caltech)

In 2016, Gukov, Putrov and Vafa conjectured the existence of invariants of 3-manifolds which are q-series with integer coefficients. They are expected to have a categorification in a sense of Khovanov homology. More recently, in 2019, Gukov and Manolescu studied the analogue of GPV invariants for knot complements and their behavior under Dehn surgery. 

In this talk, I will review what is known about these conjectural invariants, recalling the results by Gukov-Pei-Putrov-Vafa and Gukov-Manolescu, and then I will discuss a generalization of these results to arbitrary gauge group.