MAT 648, Fall 2014

MAT 648: Mirror Symmetry for Gromov-Witten Invariants

Stony Brook Fall 2014

Announcements

Here is general information about the course.

Here are Notes on Mirror Symmetry (updated 10/11/15). The last update consists of Sections 2.3 and 2.4. It covers the lecture on 10/14, but still only the beginning of the lecture on 10/09; hopefully, the rest of the lectures on 10/09,16 will appear this weekend. Sections 1 and 4 should be complete, but may be revised in the future. Please let me know if you have any comments or corrections (however minor).

Course Instructor

Name: Aleksey Zinger E-mail: azinger@math Phone: 632-8288
Office: Math Tower 3-111 Office Hours: W 9-10 in P-143, 10-12 on 3-111

Tentative Schedule

Date	Topic	Read
08/26, Tu	Introduction	[Z]: Section 1.1
08/28, Th	Classifying spaces	[Z]: Sections 1.1,1.2
09/02, Tu	no class: student holiday
09/04, Th	Group cohomology	[Z]: Sections 1.2,1.3
09/09, Tu	Equivariant cohomology	[Z]: Sections 1.3-1.5
09/11, Th	Equivariant vector bundles	[Z]: Section 1.4,1.5
09/16, Tu	Equivariant pushforward	[Z]: Sections 1.6,1.7
09/18, Th	Equivariant pushforward	[Z]: Sections 1.6,1.7
09/23, Tu	Equivariant localization theorem: statement	[Z]: Sections 1.8,1.9
09/25, Th	Equivariant localization theorem: proof	[Z]: Sections 1.8,1.9
09/30, Tu	SCGP Workshop
10/02, Th	SCGP Workshop
10/07, Tu	Quantum Lefschetz Hyperplane Principle	[Z]: Sections 2.0-2.2
10/09, Th	A symplectic perspective	[MS]: Section 7.1-7.3
10/14, Tu	Gromov's convergence topology	[Z]: Sections 2.3,2.4
10/16, Th	Linearizations	[MS]: Sections 2.5,3.1,3.2,6.1 [MirSym]: Chapter 24
10/21, Tu	Proof of QLHP and AG perspective	[MS]: Section 7.3, [FP]: Sections 0-7
10/23, Th	Torus actions on moduli spaces	[MirSym]: Section 27.3
10/28, Tu	Weights of torus actions	[MirSym]: Sections 27.2,27.4
10/30, Th	Some computations	[MirSym]: Sections 27.5
11/04, Tu	Givental's J-function	[Z]: Sections 4.1-4.3
11/06, Th	Givental's polynomiality property	[Z]: Section 4.4
11/11, Tu	Givental's rigidity property	[Z]: Section 4.4
11/13, Th	Recursivity for J-function	[Z]: Section 4.6
11/18, Tu	Polynomiality for J-function	[Z]: Section 4.7
11/20, Th	Invariance of rigidity conditions	[Z]: Section 4.5
11/25, Tu	An overview	-

References

[AB] M. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28.
[BCFK] A. Bertram, I. Ciocan-Fontanine, and B. Kim, Two proofs of a conjecture of Hori and Vafa, Duke Math. J. 126 (2005), no. 1, 101-136.
[CdGP] P. Candelas, X. de la Ossa, P. Green, and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B359 (1991), 21–74.
[MirSym] K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa, R. Vakil, and E. Zaslow, Mirror Symmetry, Clay Math. Inst., AMS 2003.
[K] B. Kim, Quantum hyperplane section theorem for homogeneous spaces, Acta Math. 183 (1999), no. 1, 71–99.
[MS] D. McDuff and D. Salamon, J-Holomorphic Curves and Symplectic Topology, 2nd Ed., AMS 2012.
[Z] A. Zinger, Notes on Mirror Symmetry.

This page is maintained by Aleksey Zinger.

Last modified: November 15, 2014.