Enumerative Geometry Zoominar, Fall 2020

Woonam Lim

This quarter, we plan to have a paper reading seminar on Donaldson-Thomas theory of 3-fold and CY 4-fold. Occasionally, we will have outside speakers speaking about their research.

Organizational: Wednesday 1:00 - 2:30 at Zoom

List of lectures:

  1. Oct. 7. Woonam Lim. GW/DT theory and MNOP conjecture. (Notes)
  2. Oct. 14. Michail Savvas. Higher structures in moduli theory. (Notes)
  3. Oct. 21. Michail Savvas. Higher structures in moduli theory, continued.
  4. Oct. 28. Bochao Kong. Behrend function and DT type invariants & degree 0 MNOP conjecture. (Notes)
  5. Nov. 4. Patrick Girardet. motivic degree zero Donaldson-Thomas invariants. (Notes)
  6. Nov. 11. Shubham Sinha. Edidin-Graham's characteristic class.
  7. Nov. 18. Shubham Sinha. Edidin-Graham's characteristic class, continued.
  8. Nov. 25. (Special talk) Ming Zhang. Verlinde/Grassmannian Correspondence.
  9. Dec. 2. (Special talk) Svetlana Makarova. Moduli spaces of stable sheaves over quasipolarized K3 surfaces, and Strange Duality.
  10. Dec. 9. Woonam Lim. Enumerative geometry of CY 4-folds. (Notes)

List of references in order:

  1. [MNOP1] Gromov-Witten theory and Donaldson-Thomas theory, I.
  2. [MNOP2] Gromov-Witten theory and Donaldson-Thomas theory, II.
  3. [Joyce] A classical model for derived critical loci.
  4. [Toen] Derived algebraic geometry.
  5. [Toen, Vezzosi] Homotopical Algebraic Geometry II: geometric stacks and applications.
  6. [Pantev, Toen, Vaquie, Vezzosi] Shifted simplectic structures.
  7. [Brav, Bussi, Joyce] A 'Darboux theorem' for derived schemes with shifted symplectic structure.
  8. [Ciocan-Fontanine, Kapranov] Derived Quot schemes.
  9. [Heleodoro] Representability of the derived Quot scheme.
  10. [Cao, Gross, Joyce] Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds.
  11. [Kiem, Li] Categorification of Donaldson-Thomas invariants via perverse sheaves.
  12. [Kahn] Virtual fundamental classes of derived stacks I.
  13. [Joyce] D-manifolds and d-orbifolds: a theory of derived differential geometry.
  14. [Behrend] Donaldson-Thomas invariants via microlocal geometry.
  15. [Behrend, Fantechi] Symmetric Obstruction Theories and Hilbert Schemes of Points on Threefolds.
  16. [Behrend, Bryan, Szendroi] Motivic degree zero Donaldson-Thomas invariants.
  17. [Edidin, Graham] Characteristic Classes and Quadric Bundles.
  18. [Oh, Thomas] Counting sheaves on Calabi-Yau 4-folds, I.
  19. [Ruan, Zhang] Verlinde/Grassmannian Correspondence and Rank 2 δ-wall-crossing.
  20. [Klemm, Pandharipande] Enumerative geometry of Calabi-Yau 4-folds.
  21. [Cao, Maulik, Toda] Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds.
  22. [Cao, Toda] Curve counting via stable objects in derived categories of Calabi-Yau 4-folds.