Enumerative Geometry Seminar
UCSD, Fall 2020
This quarter, we 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:
Oct. 7. Woonam Lim. GW/DT theory and MNOP conjecture. -- notes
Oct. 14. Michail Savvas. Higher structures in moduli theory. -- notes
Oct. 21. Michail Savvas. Higher structures in moduli theory, continued.
Oct. 28. Bochao Kong. Behrend function and DT type invariants & degree 0 MNOP conjecture. -- notes
Nov. 4. Patrick Girardet. motivic degree zero Donaldson-Thomas invariants. -- notes
Nov. 11. Shubham Sinha. Edidin-Graham's characteristic class.
Nov. 18. Shubham Sinha. Edidin-Graham's characteristic class, continued.
Nov. 25. (Special talk) Ming Zhang. Verlinde/Grassmannian Correspondence.
Dec. 2. (Special talk) Svetlana Makarova. Moduli spaces of stable sheaves over quasipolarized K3 surfaces, and Strange Duality.
Dec. 9. Woonam Lim. Enumerative geometry of CY 4-folds. -- notes
List of references in order:
[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 δ-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.