ICTP/IGAP Algebraic Geometry Seminar - Friday 22 April, at 14:00 (Lothar Goettsche)/hybrid

[ICTP Math Section]

ICTP/IGAP Algebraic Geometry Seminar

_PLEASE NOTE UNUSUAL SEMINAR TIME (14:00 - 15:30)_
Starts 22 Apr 2022 14:00
Ends 22 Apr 2022 15:30
Central European Time

Presence: ICTP Leonardo Da Vinci Building - Euler Lecture Room

Online:

Register in advance for this meeting:
https://zoom.us/meeting/register/tJEpfuCvpjguHdKtzcES0xzHegVySNQN0hC3
After registering, you will receive a confirmation email containing 
information about joining the meeting.

Speaker: Lothar Göttsche (ICTP)

Title: Computation of vertical Vafa-Witten invariants

Abstract: Last time we introduced nested Hilbert schemes and how one can 
express vertical Vafa-Witten as intersection numbers on nested Hilbert 
schemes.

After reviewing this we will  the sketch of proof of Laarakker's 
structure theorem for the vertical Vafa-Witten invariants, expressing 
them in terms of universal generating functions and Seiberg-Witten 
invariants. The proof uses the cobordism invariants of intersection
numbers on Hilbert schemes of points.

Then we will show how one can use this to explicitely determine the 
generating function for the Vertical-Vafa-Witten invariants, by first 
reducing to the case of toric surfaces and then localizing on Hilbert 
schemes of points on toric surfaces.
In the remaining two (2) lectures we will

(1) finish explaining the ingrediends of this  computation, and present 
the formulas for the vertical-Vafa-Witten invariants, in terms of 
modular forms

(2) state Mochizuki's formula for computing the horizontal Vafa-Witten 
invariants and use it to compute horizontal Vafa-Witten invariants.

/_Previous Lecture held on 6th of April:_/

Title: Vertical Vafa-Witten invariants and nested Hilbert schemes

Abstract: We state the structure theorem of Laarakker for the vertical 
Vafa-Witten invariants of a projective surface S. We introduce nested 
Hilbert schemes (an incidence variety in products of Hilbert schemes of 
points and curves on the surface S), and their relation to vertical 
components of Vafa-Witten moduli spaces.

We describe how the vertical Vafa-Witten invariants can be computed in 
terms of nested Hilbert schemes. We sketch the proof of Laarakker's 
structure theorem.

/This will be a hybrid seminar. All are very welcome to join either 
online or in person (if provided with a green pass). Venue: Euler 
Lecture Room (ICTP Leonardo Da Vinci Building), for those wishing to 
attend in person./

https://indico.ictp.it/event/9936/

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela