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Cell decompositions of character varieties and motivification of knot invariants

Mathematical Physics

Speaker: Anton Mellit, Vienna
Location: Zoom
Start time: Fri, May 15 2020, 11:00AM

Description

On the one side, Hausel-Letellier-Rodriguez-Villegas conjectures relate 1) cohomologies of character varieties with 2) the K-theory of Hilbert schemes of C^2. On the other side, Gorsky-Negut-Rasmussen conjectures relate 3) triply graded Khovanov homologies of links to the same K-theory 2). I will talk about an explicit geometric way to relate 1) and 3). The character varieties are stratified in such a way that strata are motivic invariants of links. I will also talk about interesting additional structure that naturally arises on these cohomologies, a part of which is the curious hard Lefschetz property. Many examples can be explicitly computed because of the mysterious parity phenomenon.



Zoom info distributed by email; contact tudor@math.ucdavis.edu with any questions.