ICTP/IGAP Algebraic Geometry Seminar - Wednesday, 16 March, at 16:00 (Lothar Goettsche)/hybrid seminar

[ICTP Math Section]

ICTP/IGAP Algebraic Geometry Seminar on "Vertical Vafa-Witten invariants"

Starts 16 Mar 2022 16:00
Ends 16 Mar 2022 17:00
Central European Time

Presence: ICTP Leonardo Building - Luigi Stasi Seminar Room

Online:
Register in advance for this meeting:
https://zoom.us/meeting/register/tJIkfuuprjgjGNcgVmSaMlPCelgrDAqtiUSK
After registering, you will receive a confirmation email containing 
information about joining the meeting.

Speaker Lothar Goettsche (ICTP)

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.

https://indico.ictp.it/event/9913/

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