## MAT 648: Mirror Symmetry for Gromov-Witten Invariants
## Stony Brook Fall 2014 |
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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).

*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

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 | ||

09/23, Tu | Equivariant localization theorem: statement | [Z]: Sections 1.8,1.9 |

09/25, Th | Equivariant localization theorem: proof | |

09/30, Tu | SCGP Workshop | |

10/02, Th | ||

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 | - |

- [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.