The 5th Workshop for Young Symplectic Geometers
February 24–26, 2023
Sungkyunkwan University, Seoul, Korea
sponsored byNational Research Foundation of Korea
QSMS Center for Quantum Structures in Modules and Spaces
Invited Speakers
- Youngjin Bae (Incheon National University)
- Jungsoo Kang (Seoul National University)
- Hyunki Min (UCLA)
Organizers
- Byung Hee An (Kyungpook National University)
- Youngjin Bae (Incheon National University)
- Yunhyung Cho (Sungkyunkwan University)
Venue
- Hoam Bldg., Room #50106
- Sungkyunkwan University, Humanities and Social Sciences Campus (Hyehwa), Seoul, Korea
Talk Schedule
| February 24 (Fri) | February 25 (Sat) | February 26 (Sun) | |
|---|---|---|---|
| 10:00 – 10:30 | Arrival and Registration |
Hyunki Min (II) | Youngjin Bae (III) |
| 10:30 – 11:00 | Question Session | ||
| 11:00 – 11:30 | Youngjin Bae (II) | Jungsoo Kang (III) | |
| 11:30 – 12:00 | Question Session | Closing Remark | |
| 12:00 – 14:00 | Lunch | ||
| 14:00 – 14:30 | Opening Remark | Free Discussion | |
| 14:30 – 15:00 | Youngjin Bae (I) | Jungsoo Kang (II) | |
| 15:00 – 15:30 | Question Session | ||
| 15:30 – 16:00 | Hyunki Min (I) | Hyunki Min (II) | |
| 16:00 – 16:30 | Question Session | ||
| 16:30 – 17:00 | Jungsoo Kang (I) | Free Discussion & Question Session |
|
| 17:00 – 17:30 | Question Session | ||
| 18:00 - | Workshop Dinner | Departure | |
* The schedule may vary.
Title & Abstract
Abstracts
- Speaker
- Youngjin Bae (Incheon National University)
- Title
- Lagrangain fillings for Legendrian links of Dynkin type
- Abstract
We will introduce Legendrian links of finite and affine type, and then argue that there are at least as many Lagrangian fillings as seeds in the corresponding cluster structure. The main ingredients are N-graphs developed by Casals-Zaslow, and cluster structures by Fomin-Zelevinsky. This is a joint work with Byung Hee An and Eunjeong Lee.
Talk 1: We review the definition and basic properties of Legendrians in contact spaces, especially in dimension 3 and 5. In order to present Legendrian links and surfaces up to Legendrian isotopy, we will introduce N-graphs and their moves.
Talk 2: We investigate the flag moduli of Legendrian obtained by rainbow closure of positive braids which admits a cluster structure. We consider the Coxeter mutation on the seed pattern of finite/affine Dynkin type which is essential in our construction.
Talk 3: In order to connect N-graphs and cluster structure in a more concrete way, we construct seeds in cluster structure from N-graphs and Flag moduli. We also introduce Legendrian realization of Coxeter mutation in N-graphs.
- Speaker
- Jungsoo Kang (Seoul National University)
- Title
- Floer homology of prequantization spaces
- Abstract
- In this series of lectures, I will discuss the Rabinowitz Floer homology (RFH in short, aka symplectic homology) of prequantization spaces. Prequantization spaces are circle bundles over closed integral symplectic manifolds which have canonical contact structures. One natural setting in which RFH for a prequantization space is defined is when it admits a Liouville filling. I will explain the construction of a Gysin-type long exact sequence relating RFH for a Liouville filling of a prequantization bundle and the quantum homology of the base manifold. On the other hand, prequantization bundles carry natural (non-exact) symplectic fillings, namely the associated complex line bundles. I will introduce filtrations for the chain complex of RFH for complex line bundles and present computational results. This lecture series is based on joint work with Peter Albers, Joonghyun Bae, and Sungho Kim.
- Speaker
- Hyungki Min (UCLA)
- Title
- Handlebody construction of the complex projective plane
- Abstract
- Weinstein handle diagrams provide a powerful and convenient tool for working with symplectic manifolds with boundary. This motivates the problem of building an analogous theory of handle decompositions that record the data of a closed symplectic manifold. In these talks, we present handlebody descriptions of symplectic embeddings of rational homology balls into the complex projective plane, which provide infinitely many symplectic handlebody decompositions of a closed symplectic 4-manifold. We will also discuss a topological interpretation of almost toric fibrations in terms of symplectic handles.
Contact
- Byung Hee An (anbyhee_at_knu.ac.kr)
- Youngjin Bae (yjbae_at_inu.ac.kr)
- Yunhyung Cho (yunhyung_at_skku.ac.kr)
Sponsored by
- National Research Foundation of Korea(NRF)
- QSMS Center for Quantum Structures in Modules and Spaces
