The 6th Workshop for Young Symplectic Geometers
June 9–11, 2023
Pusan National University, Busan, Korea
sponsored byNational Research Foundation of Korea
QSMS Center for Quantum Structures in Modules and Spaces
Invited Speakers
- Byunghee An (Kyungpook National University)
- Kyungmin Rho (Seoul National University)
- Pyongwon Suh (The Chinese University of Hong Kong)
Organizers
- Byung Hee An (Kyungpook National University)
- Youngjin Bae (Incheon National University)
- Yunhyung Cho (Sungkyunkwan University)
- Yoosik Kim (Pusan National University)
Venue
- #110, Comprehensive Research Bldg. 607
- Pusan National University, Busan, Korea
Talk Schedule
| June 9 (Fri) | June 10 (Sat) | June 11 (Sun) | |
|---|---|---|---|
| 10:00 – 10:30 | Arrival and Registration |
Suh (II) | Rho (III) |
| 10:30 – 11:00 | Question Session | ||
| 11:00 – 11:30 | Rho (II) | An (III) | |
| 11:30 – 12:00 | Question Session | Closing Remark | |
| 12:00 – 14:00 | Lunch | ||
| 14:00 – 14:30 | An (II) | Free Discussion | |
| 14:30 – 15:00 | Opening Remark | Question Session | |
| 15:00 – 15:30 | Suh (I) | Suh (II) | |
| 15:30 – 16:00 | Question Session | ||
| 16:00 – 16:30 | Rho (I) | Free Discussion & Question Session |
|
| 16:30 – 17:00 | Question Session | ||
| 17:00 – 17:30 | An (I) | ||
| 17:30 – 18:00 | Question Session | ||
| 18:00 - | Workshop Dinner | Departure | |
* The schedule may vary.
Title & Abstract
Abstracts
- Speaker
- Byunghee An (Kyungpook National University)
- Title
- Legendrian knot invariants
- Abstract
- Legendrian knots are 1-dimensional Legendrian submanifolds in the three sphere with the standard contact structures, which can be used to obtain arbitrary contact three manifolds by the surgery process. It is also known that for a fixed topological knot type, there are infinitely many pairwise distinct Legendrian knots of given topological knot type and therefore it is not easy to distinguish Legendrian knots. In this series of talks, I will introduce both classical and modern invariants of Legendrian knots and how they are related to each other.
- Speaker
- Kyungmin Rho (Seoul National University)
- Title
- Homological Mirror Symmetry and Geometry of Degenerate Cusp Singularities
- Abstract
We introduce several geometric and algebraic concepts related to homological mirror symmetry "Pair-of-pants surface (A-side) <-> Degenerate cusp singularity xyz=0 (B-side)" and find their relations.
Talk 1: Fukaya category, matrix factorizations and Cohen-Macaulay modules
We review the Fukaya category (A-side), and explain its relation to matrix factorizations and Cohen-Macaulay modules (B-side).
Talk 2: Representation of Cohen-Macaulay modules
We explore the representation and classification of Cohen-Macaulay modules over degenerate cusp singularities (B-side). Then we establish a correspondence with the geodesics equipped with holonomy (A-side).Talk 3: Degenerate vector bundles
We develop a new concept of degenerate vector bundles to provide a geometric construction of Cohen-Macaulay modules (B-side).This talk is based on
(1) joint works with Cheol-Hyun Cho, Wonbo Jeong, and Kyoungmo Kim,
(2) my upcoming thesis.
- Speaker
- Pyongwon Suh (CUHK)
- Title
- The Coherent-Constructible Correspondence for toric fiber bundles
- Abstract
- The Coherent-Constructible Correspondence(CCC) is a version of Homological Mirror Symmetry for toric varieties which intertwines with a sheaf theoretical approach to symplectic geometry. It states an equivalence between the derived category of a toric variety and the category of certain constructible sheaves on a torus. In this talk, I will review the sheaf theoretical approach to symplectic geometry(singular support, microlocal sheaves, etc.) and CCC through concrete examples. Also, I will present my joint work with Yuxuan Hu on the family version of CCC for toric fiber bundles.
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
