Time and Place
Time: 09.09 and Every Friday 19:20-20:55 from 2024.09.27-2024.12.27 (no seminar on 09.20 and 10.04)
Place: Shuangqing Complex Building C546
Prerequisite
Algebraic geometry and symplectic geometry.
Syllabus
We will discuss following topics in quantum cohomology.
- Gamma conjecture and quantum D-module after Iritani. [1–3] (Jinghao Yu & Nantao Zhang)
- Small quantum cohomology of birational Calabi-Yau manifolds [4] (Lite Du)
- Quantum groups and quantum cohomology [5] (Linpu Gao)
More references will be given during the seminar.
Tentative schedule:
| Time | Speaker | Title |
|---|---|---|
| 2024.09.09 | Nantao Zhang | Introduction to Quantum Cohomology |
| 2024.09.27 | Jinghao Yu | Gamma conjecture I |
| 2024.10.11 | Nantao Zhang | Gamma conjecture II |
| 2024.10.18 | Jinghao Yu | Gamma conjecture III |
| 2024.10.25 | Linpu Gao | Quantum groups and quantum cohomology I |
| 2024.11.01 | Linpu Gao | Quantum groups and quantum cohomology II |
| 2024.11.08 | Linpu Gao | Quantum groups and quantum cohomology III |
| 2024.11.15 | Lite Du | Quantum cohomology of birational Calabi-Yau I |
| 2024.11.22 | Lite Du | Quantum cohomology of birational Calabi-Yau II |
| 2024.11.29 | Lite Du | Quantum cohomology of birational Calabi-Yau III |
| 2024.12.06 | Nantao Zhang | Quantum cohomology of blowup I |
| 2024.12.13 | Nantao Zhang | Quantum cohomology of blowup II |
| 2024.12.20 | Nantao Zhang | Quantum cohomology of blowup III |
References
[1]
Iritani, H (2022 ). Gamma classes and quantum cohomology. Proceedings of International Congress of Mathematics. International Mathematical Union. 4 2552–74
[2]
Galkin, S, Golyshev, V and Iritani, H (2016 ). Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures. Duke mathematical journal. Duke University Press. 165 2005–77. https://projecteuclid.org/journals/duke-mathematical-journal/volume-165/issue-11/Gamma-classes-and-quantum-cohomology-of-Fano-manifolds--Gamma/10.1215/00127094-3476593.full
[4]
McLean, M (2020 ). Birational Calabi-Yau manifolds have the same small quantum products. Ann. of math. (2). 191. https://projecteuclid.org/journals/annals-of-mathematics/volume-191/issue-2/Birational-Calabi-Yau-manifolds-have-the-same-small-quantum-products/10.4007/annals.2020.191.2.4.full
[5]
Maulik, D and Okounkov, A (2018 ). Quantum Groups and Quantum Cohomology. http://arxiv.org/abs/1211.1287
Organizer
Nantao Zhang(张南涛)
You may join by contacting me by email znt21 (at) mails.tsinghua.edu.cn.