ICTP/IGAP Algebraic Geometry Seminar - Wednesday, 2 March, at 16:00 (Lothar Goettsche)/hybrid seminar

[ICTP Math Section]

ICTP/IGAP Algebraic Geometry Seminar on "Localization and virtual 
localization, and Vafa-Witten generating function"

Speaker: Lothar GOETTSCHE (ICTP)

Starts 2 Mar 2022 16:00
Ends 2 Mar 2022 17:00
Central European Time

Hybrid seminar

Presence: Luigi Stasi Seminar Room (ICTP Leonardo Building)


Online:
Register in advance for this meeting:
https://zoom.us/meeting/register/tJcvdOCuqDIoH9xPSv9b8G-Yf_J_K4BSm9Ji
After registering, you will receive a confirmation email containing 
information about joining the meeting.

Abstract: We define Vafa-Witten invariants via formal virtual 
localization. First we review localization and virtual localization with 
respect to $C^*$-actions. We describe the fixpoint locus of the $C^*$ 
action on the Vafa-Witten moduli space, and its decomposition into 
components corresponding to the partitions of the rank r.
We introduce the Vafa-Witten generating function, and its decomposition 
corresponding to the components of the fix point 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.

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 
lecture room (ICTP Leonardo Da Vinci Building), for those wishing to 
attend in person.

http://indico.ictp.it/event/9906/

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ICTP Mathematics Group
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