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 Beauville-Voisin 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 K-theoretic
Donaldson-Thomas theory of points (special lecture)
-
Apr 28. Shubham Sinha - Stable quasimaps to GIT quotients
-
May 5. Woonam Lim - Kawai-Yoshioka's formula and Hodge numbers of
moduli
spaces of stable pairs on K3 surfaces
-
May 12. Michail Savvas - Fourier-Mukai 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
Donaldson-Thomas theory of
Calabi-Yau 4-folds
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 Donaldson-Thomas
invariants
-
Nov 11. Shubham Sinha - Edidin-Graham's characteristic class
-
Nov 18. Shubham Sinha -
DT invariants of CY 4-folds
-
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 4-folds
References:
-
[MNOP1] Gromov-Witten
theory and Donaldson-Thomas theory, I
-
[MNOP2] Gromov-Witten
theory and Donaldson-Thomas 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
-
[Ciocan-Fontanine,
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 Calabi-Yau 4-folds
-
[Kiem, Li]
Categorification of Donaldson-Thomas invariants via perverse sheaves
-
[Kahn] Virtual
fundamental classes of derived stacks I
-
[Joyce]
D-manifolds and d-orbifolds:
a theory of derived differential geometry
-
[Behrend]
Donaldson-Thomas invariants via microlocal geometry
-
[Behrend, Fantechi]
Symmetric Obstruction Theories and Hilbert Schemes of Points on
Threefolds
-
[Behrend, Bryan,
Szendroi] Motivic degree zero Donaldson-Thomas invariants
-
[Edidin, Graham]
Characteristic Classes and Quadric Bundles
-
[Oh, Thomas] Counting
sheaves on Calabi-Yau 4-folds, I
-
[Ruan, Zhang]
Verlinde/Grassmannian Correspondence and rank 2 \delta wall-crossing
-
[Klemm,
Pandharipande] Enumerative geometry of Calabi-Yau 4-folds
-
[Cao, Maulik, Toda]
Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
-
[Cao, Toda] Curve
counting via stable objects in derived categories of Calabi-Yau 4-folds
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 - Gromov-Witten theory and Noether-Lefschetz
theory
Participants: Patrick Girardet, Bochao Kong, Dragos Oprea,
Michail Savvas, Shubham Sinha
References: