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Title:
Categorified Wall-Crossing With Twisted Masses
Speaker:
Abstract:
The talk will discuss "categorification," or more accurately, "braneification" of wall-crossing formulae (wcf). We review the general statement of the 2d4d wcf. Then we review and refine the Cecott-Vafa wcf in 2d Landau-Ginzburg models. We further refine it in the context of the A-infinity category of interfaces using ``S wall interfaces'' for ``S-wall-crossing.'' Finally, we discuss the effect of twisted masses, which lead to some novel new phenomena, including K-wall interfaces, closely related to Koszul duality of algebras. Most of the talk is a review of work done with D. Gaiotto and E. Witten pre-2015. Some of the material presented comes from unpublished work with T. Dimofte and D. Gaiotto from 2016, together with more recent work in progress with Rutgers graduate student Ahsan Khan. The subject is closely related to spectral networks, hence relevant to this workshop on holomorphic differentials. However, the practice run at a Rutgers group meeting took over 2 hours, so much material, including the relation to spectral networks will have to be omitted.
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