ICTP/IGAP Seminar on Algebraic Geometry - Lecture Series - Wednesday, 26 January, at 16:00 (Alina MARIAN) - Online and Presence

[ICTP/math - Mabilo Koutou]

ICTP/IGAP seminar on Algebraic Geometry (2nd talk by Alina Marian)

The seminar will consist of lecture series by Alina Marian* and by  Lothar
Goettsche (of which the abstracts are below), and talks by  Postdocs and
Faculty on their research.

Toward the cohomology and Chow rings of moduli spaces of sheaves (Alina 
Marian).

A seminar direction will examine the problem of understanding Lie  algebra
actions on the cohomology and Chow rings of moduli spaces of  sheaves
interms of the Chern classes of the universal sheaf. One
classical action on cohomology is the Lefschetz sl(2) associated with an 
ample divisor class on a projective variety. For moduli spaces of  sheaves
over curves and surfaces, Grothendieck's standard conjectures  are often
known to hold, in particular Lefschetz sl(2) actions should be 
expressible via algebraic correspondences. Nevertheless there are very 
few explicit algebraic constructions of the Lefschetz operators.
Progress in this direction would have important applications, not least 
to holomorphic symplectic geometry; the seminar will explain this circle 
of ideas.

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Virtual invariants of moduli spaces of sheaves on surfaces and
Vafa-Witten invariants (Lothar Goettsche).

Another direction of the seminar will be virtual invariants of moduli 
spaces of sheaves on surfaces and Vafa-Witten invariants. Moduli spaces 
of sheaves on surfaces with $p_g>0$ tend to be singular, but they carry  a
so-called perfect obstruction theory, which allows to define virtual 
versions of the standard topological invariants of smooth varieties,  e.g.
the virtual Euler number. In 1994 Vafa and Witten gave a formula  for
"Euler numbers" of moduli spaces of rank 2 sheaves on surfaces.  Recently
a mathematical definition of these Vafa-Witten invariants was  given in
arbitrary rank by Tanaka and Thomas in terms of moduli spaces  of Higgs
pairs. We will review the definition of these invariants and  their
relation to virtual Euler numbers of moduli spaces of sheaves on 
surfaces, and show computations of these invariants leading to conjectural
generating functions in terms of modular functions.

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The title for the 2nd talk on Wednesday 26 January, at 16:00:

Speaker: Alina Marian (Northeastern University)

Title: The sl(2) action on the Chow ring of an abelian variety

Register in advance for this meeting:

Register in advance for this meeting:
https://zoom.us/meeting/register/tJUvd-yurjkrGdHTTDO2mFbC5qPgxAW-B4wj

After registering, you will receive a confirmation email containing
information about joining the meeting.

http://indico.ictp.it/event/9857/

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, for those wishing to attend in person.


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

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