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M-Seminar: Categorification of Donaldson-Thomas invariants

Speaker: Marco Robalo, Sorbonne Universite

Abstract: Given a (-1)-shifted derived scheme $X$ with a convenient orientation data (in the sense of Kontsevich-Soibelman), Brav-Bussi-Dupont-Joyce-Szendroi (BBDJS) constructed a perverse sheaf over $X$ and whose Euler characteristic recovers Behrend's counting of Donaldson-Thomas invariants. The BBDJS construction uses a Darboux local form for (-1)-shifted symplectic schemes: locally they are all derived critical loci of a function $f$ on a smooth scheme $U$ and the DT-invariants are obtained from the Euler characteristic of the sheaf of vanishing cycles of $f$. In this talk I will describe an ongoing joint work with B. Hennion and J. Holstein where we propose a strategy based on To\"en-Vezzosi derived foliations, to glue over $X$ a sheaf of 2-periodic dg-categories locally modeled on the categories of matrix factorisations $MF(U,f)$. In particular, our strategy allows us to recover the construction of BBDJS.

Dial-In Information

Zoom link

Meeting ID: 958 3425 4862

Thursday, September 29 at 12:30pm to 2:00pm



Mathematics, Department of
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