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.