Starts 16 Mar 2022 16:00
Ends 16 Mar 2022 17:00
Central European Time
Leonardo Building - Luigi Stasi Seminar Room
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Abstract: We describe the components corresponding of the fixpoint locus on the Vafa-Witten moduli space.
We introduce the Vafa-Witten generating function, and its decomposition corresponding to the components of the fixpoint locus. In particular we have the horizontal component, corresponding to the partition (r), which is the moduli space of stable sheaves, and the vertical component, corresponding to the partition (1,..,1).
We show that the contribution to the horizontal component to the VW invariants is the virtual Euler number of the moduli space of sheaves.
We state the Vafa-Witten predictions for the modularity of the Vafa-Witten generating function.
We state the structure theorem of Laaracker for the vertical Vafa-Witten invariants, and give conjectural formulas for the vertical Vafa-Witten invariants.
Finally we conjecture an analogue of Laaracker's structure theorem also for the horizontal invariants.
This will be a hybrid seminar. All are very welcome to join either online or in person (if provided with a green pass). Venue: Luigi Stasi Seminar Room (ICTP Leonardo Da Vinci Building), for those wishing to attend in person.