Lectures:

Oct 29. Bochao Kong  Virtual fundamental classes

Nov 5. Shubham Sinha  Examples of virtual fundamental classes in
enumerative geometry

Nov 12. Woonam Lim  VafaWitten invariants of surfaces

Nov 19. Woonam Lim  VafaWitten invariants of surfaces II

Nov 26. Michail Savvas  Ktheoretic refined VafaWitten
invariants

Dec 3. Michail Savvas  Ktheoretic refined VafaWitten
invariants II
Participants: Patrick Girardet, Bochao Kong, Woonam Lim, Dragos
Oprea, Michail Savvas, Shubham Sinha
References:

[Behrend, Fantechi]
The intrinsic normal cone

[Siebert] Virtual
fundamental classes, global normal cones and Fulton's
canonical classes

[Tanaka, Thomas]
VafaWitten invariants for projective surfaces I: stable
case

[Thomas] A Ktheoretic
Fulton class

[Thomas] Equivariant
Ktheory and refined VafaWitten invariants
Lectures:

Jan 14. Woonam Lim  Recursive structure on Hilbert scheme of points
on surfaces

Jan 21. Bochao Kong  On the product identities and the Chow rings
of holomorphic symplectic varieties

Jan 28. Patrick Girardet  Heisenberg action on cohomology of
Hilbert scheme of points on surfaces

Feb 4. Shubham Sinha  TQFT defined by Quot schemes on curves

Feb 10. Patrick Girardet  Tautological classes and Lehn's formula
in cohomology

Feb 20. Sayanta Mandal  Betti numbers of the moduli space of
sheaves on projective plane (special lecture)

Feb 25. Michail Savvas  Lehn's formula in Chow group and its
application to BeauvilleVoisin conjecture

Mar 3. Woonam Lim  Introduction to motives
Participants: Patrick Girardet, Bochao Kong, Woonam Lim, Dragos Oprea,
Michail Savvas, Shubham Sinha
References:

[Ellignsrud, Gottsche,
Lehn] On the Cobordism Class of the Hilbert
Scheme of a Surface

[Barros, Flapan, Marian,
Silversmith] On product identities and the
Chow rings of holomorphic symplectic varieties

[Nakajima] Heisenberg
Algebra and Hilbert Schemes of Points on
Projective Surfaces

[Marian, Oprea] GL Verlinde
numbers and Grassmann TQFT

[Lehn] Chern Classes of
Tautological Sheaves on Hilbert Schemes

[Mandal] On the
stabilization of the
Betti numbers of the moduli
space of sheaves on P2

[Maulik, Negut] Lehn's
formula in Chow and Conjectures of Beauville
and Voisin

[Murre, Nagel, Peters]
Lectures on theory of pure motives
Enumerative Geometry Seminar  Spring 2020
Sheaves on K3 surfaces
Lectures:

Apr 7. Patrick Girardet  Decomposition of Chow groups of abelian
varieties

Apr 14. Bochao Kong  Some examples of Mukai's reflections on K3
surfaces

Apr 21. Andrea Ricolfi  Higher rank Ktheoretic
DonaldsonThomas theory of points (special lecture)

Apr 28. Shubham Sinha  Stable quasimaps to GIT quotients

May 5. Woonam Lim  KawaiYoshioka's formula and Hodge numbers of
moduli
spaces of stable pairs on K3 surfaces

May 12. Michail Savvas  FourierMukai transforms for elliptic
surfaces

May. 19. Patrick Girardet  Refined Verlinde formulas for moduli of
sheaves
on K3 surfaces

June. 9. Shubham Sinha  Quantum cohomology of Grassmannians
Participants: Patrick Girardet, Bochao Kong, Woonam Lim, Dragos Oprea,
Michail Savvas, Shubham Sinha
References:
Enumerative Geometry Seminar  Fall 2020
DonaldsonThomas theory of
CalabiYau 4folds
Participants: Patrick Girardet, Bochao Kong, Woonam Lim, Dragos Oprea,
Michail Savvas, Shubham Sinha
Lectures:

Oct 7. Woonam Lim  GW/DT theory and MNOP conjecture

Oct 14. Michail Savvas  Higher structures in moduli theory

Oct 21. Michail Savvas  Higher structures in moduli theory II

Oct 28. Bochao Kong  Behrend function and DT type invariants &
the degree
0
MNOP conjecture

Nov 4. Patrick Girardet  Motivic degree zero DonaldsonThomas
invariants

Nov 11. Shubham Sinha  EdidinGraham's characteristic class

Nov 18. Shubham Sinha 
DT invariants of CY 4folds

Nov 25. Ming Zhang  Verlinde/Grassmannian correspondence
(special lecture)

Dec 2. Svetlana Makarova  Moduli spaces of stable sheaves
over quasipolarized K3 surfaces, and Strange Duality (special
lecture)

Dec 9. Woonam Lim  Enumerative geometry of CY 4folds
References:

[MNOP1] GromovWitten
theory and DonaldsonThomas theory, I

[MNOP2] GromovWitten
theory and DonaldsonThomas theory, II

[Joyce] A classical model
for derived critical loci

[Toen] Derived algebraic
geometry

[Toen, Vezzosi]
Homotopical Algebraic Geometry II: geometric stacks and applications

[Pantev, Toen, Vaquie,
Vezzosi] Shifted simplectic structures

[Brav, Bussi, Joyce] A
'Darboux theorem' for derived schemes with shifted symplectic structure

[CiocanFontanine,
Kapranov] Derived Quot schemes

[Heleodoro]
Representability of the derived Quot scheme

[Cao, Gross, Joyce]
Orientability of moduli spaces of Spin(7)instantons and coherent sheaves
on CalabiYau 4folds

[Kiem, Li]
Categorification of DonaldsonThomas invariants via perverse sheaves

[Kahn] Virtual
fundamental classes of derived stacks I

[Joyce]
Dmanifolds and dorbifolds:
a theory of derived differential geometry

[Behrend]
DonaldsonThomas invariants via microlocal geometry

[Behrend, Fantechi]
Symmetric Obstruction Theories and Hilbert Schemes of Points on
Threefolds

[Behrend, Bryan,
Szendroi] Motivic degree zero DonaldsonThomas invariants

[Edidin, Graham]
Characteristic Classes and Quadric Bundles

[Oh, Thomas] Counting
sheaves on CalabiYau 4folds, I

[Ruan, Zhang]
Verlinde/Grassmannian Correspondence and rank 2 \delta wallcrossing

[Klemm,
Pandharipande] Enumerative geometry of CalabiYau 4folds

[Cao, Maulik, Toda]
Stable pairs and GopakumarVafa type invariants for CalabiYau 4folds

[Cao, Toda] Curve
counting via stable objects in derived categories of CalabiYau 4folds
Lectures:

Apr 13. Shubham Sinha  Divisors on moduli spaces of genus 0 stable
maps
to
projective space

Apr 20. Bochao Kong  Relations in the tautological ring of the moduli
space of K3 surfaces

May 3. Patrick Girardet  Automorphisms of Hilbert schemes of
points

May 24. Shubham Sinha  The Betti numbers of the moduli space of
stable
maps to projective space
 May 31. Bochao Kong  GromovWitten theory and NoetherLefschetz
theory
Participants: Patrick Girardet, Bochao Kong, Dragos Oprea,
Michail Savvas, Shubham Sinha
References:
Participants: Patrick Girardet, Bochao Kong, Dragos Oprea, Shubham
Sinha, Ming Zhang, though everybody is welcome.