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Math Graduate Student Seminar

Wednesday, January 22, 2020
12:00pm to 1:00pm
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Linde Hall 187
3-manifolds and q-series
Sunghyuk Park, Department of Mathematics, 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. If time allows, I will also talk about a HOMFLY-PT analogue of F_K, which is a work in progress with Gruen, Gukov, Kucharski and Sulkowski.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].