Gromov-Witten theory and mirror symmetry | |
Student No.： | 50 |
Time： | Mon/Wed 13:00-14:50, 2016-02-22~ 2016-06-08 (except for public holidays) |
Instructor： | Zhengyu Zong [Tsinghua University] |
Place： | Conference Room 1, Floor 1, Jin Chun Yuan West Building |
Starting Date： | 2016-2-22 |
Ending Date： | 2016-6-8 |
Description:
In this course, I will first introduce some basic aspects of Gromov-Witten theory. Then I will discuss the Frobenius structures and quantum D-modules, which belong to the genus zero data. In the toric case, we will prove the mirror theorm which identifies the D-module structures on A-model and that of the Landau-Ginzburg B-model. Then we will move on to the higher genus case. On A-model side, we will discuss Givental’s quantization formalism, which expresses the higher genus Gromov-Witten potential in terms of abstract Frobenius structures. On B-model side, we will discuss the Eynard-Orantin theory of spectral curves and its relation to Givental’s formalism. For toric Calabi-Yau 3-folds/3-orbifolds, we will prove the Remodeling Conjecture which identifies the all genus open-closed Gromov-Witten potentials with the Eynard-Orantin invariants of the mirror curves. We will discuss the relation between the mirror curve and the Landau-Ginzburg B-model in the proof of the Remodeling Conjecture.
Prerequisite:
Some basic algebraic geometry and complex analysis
Reference:
K. Hori et al. “Mirror Symmetry” Clay Mathematics Monographs, 1. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2003. xx+929 pp. ISBN: 0-8218-2955-6
Specific references will be given during the lectures.