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]


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