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SUMMARY:Lothar Goettsche (https://www.ictp.it/phonebook/person?id=2630)
DTSTART:20220422T120000Z
DTEND:20220422T133000Z
DTSTAMP:20260404T084515Z
UID:ICTP-IGAP/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ICTP-IGAP/1/
 ">Computation of vertical Vafa-Witten invariants</a>\nby Lothar Goettsche 
 (https://www.ictp.it/phonebook/person?id=2630) as part of ICTP/IGAP Algebr
 aic Geometry Seminar\n\n\nAbstract\nLast time we introduced nested Hilbert
  schemes and how one can express vertical Vafa-Witten as intersection numb
 ers on nested Hilbert schemes.\n\nAfter reviewing this we will  the sketch
  of proof of Laarakker's structure theorem for the vertical Vafa-Witten in
 variants\, expressing them in terms of universal generating functions and 
 Seiberg-Witten invariants. The proof uses the cobordism invariants of inte
 rsection\nnumbers on Hilbert schemes of points.\n\nThen we will show how o
 ne can use this to explicitely determine the generating function for the V
 ertical-Vafa-Witten invariants\, by first reducing to the case of toric su
 rfaces and then localizing on Hilbert schemes of points on toric surfaces.
 \n\nIn the remaining two (2) lectures we will\n\n(1) finish explaining the
  ingrediends of this  computation\, and present the formulas for the verti
 cal-Vafa-Witten invariants\, in terms of modular forms\n\n(2) state Mochiz
 uki's formula for computing the horizontal Vafa-Witten invariants and use 
 it to compute horizontal Vafa-Witten invariants.\n\nPrevious Lecture held 
 on 6th of April:\n\nTitle: Vertical Vafa-Witten invariants and nested Hilb
 ert schemes\n\nAbstract: We state the structure theorem of Laarakker for t
 he vertical Vafa-Witten invariants of a projective surface S. We introduce
  nested Hilbert schemes (an incidence variety in products of Hilbert schem
 es of points and curves on the surface S)\, and their relation to vertical
  components of Vafa-Witten moduli spaces.\n\nWe 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.\n\nRegister in adva
 nce for this meeting:\nhttps://zoom.us/meeting/register/tJEpfuCvpjguHdKtzc
 ES0xzHegVySNQN0hC3 \nAfter registering\, you will receive a confirmation e
 mail containing information about joining the meeting.\n\nThis will be a h
 ybrid 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.\n
LOCATION:https://researchseminars.org/talk/ICTP-IGAP/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lothar Goettsche (ICTP)
DTSTART:20220504T140000Z
DTEND:20220504T150000Z
DTSTAMP:20260404T084515Z
UID:ICTP-IGAP/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ICTP-IGAP/2/
 ">Computation of the vertical Vafa-Witten invariants II: localization on H
 ilbert schemes of points</a>\nby Lothar Goettsche (ICTP) as part of ICTP/I
 GAP Algebraic Geometry Seminar\n\n\nAbstract\nLast time we used nested Hil
 bert schemes to express vertical Vafa-Witten invariants of a surface S in 
 terms of (unknown) universal power series\, which are generating functions
  for intersection numbers on Hilbert schemes of points on S.\n\nIn this le
 cture we will reduce to the case that the surface S is toric\, and then ex
 plain how to explicitly compute the generating functions via localization.
  We will present the formulas obtained.\n\nNext time we will sketch how to
  use Mochizuki's formula to do the same for the horizontal Vafa-Witten inv
 ariants.\n\nPRESENCE: ICTP Leonardo Da Vinci Building\, Luigi Stasi Lect. 
 Room\n\nONLINE:\nRegister in advance for this meeting:\nhttps://zoom.us/me
 eting/register/tJEtd-GvqjorE9BtDAqiw4qFvW-xmtQQ0wOO \n\nAfter registering\
 , you will receive a confirmation email containing information about joini
 ng the meeting.\n
LOCATION:https://researchseminars.org/talk/ICTP-IGAP/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lothar Göttsche (ICTP)
DTSTART:20220518T143000Z
DTEND:20220518T153000Z
DTSTAMP:20260404T084515Z
UID:ICTP-IGAP/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ICTP-IGAP/3/
 ">Mochizuki's formula and the horizontal Vafa-Witten invariants</a>\nby Lo
 thar Göttsche (ICTP) as part of ICTP/IGAP Algebraic Geometry Seminar\n\n\
 nAbstract\nIn this lecture compute the horizontal Vafa-Witten invariants\,
  by using Mochizuki's formula\, which allows to reduce the computation to 
 Hilbert schemes of points.\n\nThen one can localization in a very similar 
 way as for the vertical Vafa-Witten invariants. This computation confirms 
 some of the predictions of S-duality in ranks 2 and 3.\n\nFurthermore\, co
 mbining with the computations of $S$-duality we predict the generating fun
 ctions for the horizontal Vafa-Witten invariants in rank at most 5.\n\nReg
 ister in advance for this meeting:\nhttps://zoom.us/meeting/register/tJAld
 OuoqTkiEtDRPyfZcKmD4WXPD29fNcow \nAfter registering\, you will receive a c
 onfirmation email containing information about joining the meeting.\n\nThi
 s will be a hybrid seminar. All are very welcome to join either online or 
 in person.\nVenue: Luigi Stasi Lecture Room (ICTP Leonardo Da Vinci Buildi
 ng)\, for those wishing to attend in person.\n
LOCATION:https://researchseminars.org/talk/ICTP-IGAP/3/
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