Reading Course on Quantum Cohomology (Spring 2016)
Supervisor: Davesh Maulik
Friday 9:00am at 2-346
Schedule
| Week | Date | Speaker | Topic | References |
|---|---|---|---|---|
| 1 | February 15 | Yi | Equivariant Localization | [AB], [Clay] |
| 2 | February 22 | David | Moduli space and deformation theory of stable maps | [Clay] Chapters 23-24 |
| 3 | March 4 | Dorin | GIT, stability, semi-stability | [Gin] |
| 4 | March 11 | Sid | Constructions and computations with Nakajima quiver varieties | [Gin] |
| 5 | March 18 | Yi | GW invariants, reduced / virtual fundamental class; Example: Small quantum cohomology for P^1 | [Clay], [MS2], [Giv], [Kim] |
| 6 | April 1 | David | Equivariant quantum cohomology, quantum connection, descendant GW invariants, example of P^n | [Clay] |
| 7 | April 8 | Dorin | [BMO]: Proof of main result / Toda limits | [BMO] |
| 8 | April 15 | Sid | [MO]: Stable envelopes and R-matrices | [MO] |
| 9 | April 22 | Yi | [MO]: Definition of the geometric Yangian | [MO] |
| 10 | April 29 | David | [MO]: Stable basis | [MO] |
| 11 | May 6 | Dorin | [MO]: Identification of the quantum connection with the trigonometric Casimir connection | [MO] |
| 12 | May 13 | Sid | [She]: Definition / applications of stable envelope and stable basis | [She] |
References
| Abbreviation | Source | Link |
|---|---|---|
| [AB] | Atiyah-Bott. The moment map and equivariant cohomology | |
| [BMO] | Braverman Maulik Okounkov -- Quantum cohomology of the Springer resolution | |
| [Clay] | Clay volume on mirror symmetry | Link |
| [CK] | D. Cox and S. Katz, Mirror Symmetry and Algebraic Geometry, AMS, 1999 | |
| [FP] | Fulton-Pandharipande | Link |
| [Gin] | V. Ginzburg, Lectures on Nakajima’s Quiver Varieties | arXiv:0905.0686 |
| [Giv] | Alexander Givental. Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture. | Link |
| [Kim] | Bumsig Kim. Quantum cohomology of flag manifolds G/B and quantum Toda lattices | |
| [KM] | Kontsevich-Manin | Link |
| [Mau] | Maulik. PCMI Notes | |
| [MO] | Maulik Okounkov -- Quantum Groups and Quantum Cohomology. | |
| [Mc] | McBreen -- Quantum Cohomology of Hypertoric Varieties and Geometric Representations of Yangians | |
| [MS] | McBreen Shenfeld -- Quantum Cohomology of Hypertoric Varieties | |
| [MS2] | McDuff-Salamon, J-holomorphic curves and quantum cohomology, Chapter 11 | |
| [Neg] | Quantum Algebras and Cyclic Quiver Varieties | |
| [Oko] | Okounkov -- PCMI Notes | |
| [She] | Shenfeld -- Abelianization of stable envelopes in symplectic resolutions | |
| [Su] | Su -- Equivariant quantum cohomology of cotangent bundle of G/P |