# The 2^{nd} Workshop for

Young Symplectic Geometers

**October 29–31, 2021**

Ramada Plaza Jeju Hotel, Jeju, Korea

sponsored by### National Research Foundation of Korea

##### 중견연구 2020R1A2C1A01003201 led by Byunghee An (KNU) and Youngjin Bae (INU)

##### 신진연구 2020R1C1C1A01010972 led by Yunhyung Cho (SKKU)

## Commemorative Pictures

## Invited Speakers

- Hanwool Bae (Seoul National University)
- Dongwook Choa (KIAS)
- Taekgyu Hwang (Ajou University)
- Jongmyeong Kim (IBS-CGP)
- Joontae Kim (KIAS)
- Sangjin Lee (IBS-CGP)
- Sangwook Lee (Soongsil University)

## Organizers

- Byung Hee An (Kyungpook National University)
- Youngjin Bae (Incheon National University)
- Yunhyung Cho (Sungkyunkwan University)

## Venue

- Ara Hall (8th floor)
- Ramada Plaza Jeju Hotel, Jeju, Korea

## Talk Schedule

October 29 (Fri) | October 30 (Sat) | October 31 (Sun) | |
---|---|---|---|

09:30 – 10:00 | Sangwook Lee | Hanwool Bae | |

10:00 – 10:30 | Question Session | ||

10:30 – 11:00 | Joontae Kim | Dongwook Choa | |

11:00 – 11:15 | Question Session | Closing Remark | |

11:15 - 12:00 | |||

12:00 – 14:00 | Lunch | ||

14:00 – 15:00 | Arrival and Registration |
Free Discussion & Question Session |
Departure |

15:00 – 15:15 | |||

15:15 – 15:30 | Opening Remark | ||

15:30 – 16:00 | Taekgyu Hwang | ||

16:00 – 16:30 | Question Session | ||

16:30 – 17:00 | Jongmyeong Kim | ||

17:00 – 17:30 | Question Session | ||

17:30 – 18:00 | Sangjin Lee | ||

18:00 - | Workshop Dinner |

* The schedule may vary.

## Title & Abstract (TBA)

### Research talks

- Speaker
- Hanwool Bae (Seoul National University)
- Title
- Principal Reeb orbits in the complement of divisors
- Abstract
- Let X be the complement of a divisor D in a closed symplectic manifold. We will first introduce a certain Reeb orbit in X, which we will call principal, and discuss conditions for it to define a class in the symplectic (co)homology of X. Then we will consider an A-infinity functor associated to a certain Lagrangian correspondence C from X to D. Our main concern is where the images of the principal Reeb orbit under closed-open maps are mapped to via the A-infinity functor. This talk is based on joint work with Cheol-Hyun Cho, Dongwook Choa and Wonbo Jeong.

- Speaker
- Dongwook Choa (KIAS)
- Title
- Popsicle moduli and deformation
- Abstract
- Popsicle is a version of decorated holomorphic disc invented by Abouzaid-Seidel. I briefly explain what it is and how was it used to construct a wrapped Fukaya category in their original work. Then I will explain another application, which is a construction of Fukaya-type category associated to the weighted homogeneous polynomials.

- Speaker
- Taekgyu Hwang (Ajou University)
- Title
- Seidel representation and ball embedding
- Abstract
- In the previous talk, we saw how the area of a J-holomorphic curve bounds the radius of a symplectically embedded ball. One often computes the Gromov-Witten invariants to detect such curves. Although the computation is hard, it is enough to check the invariant is non-vanishing and Seidel representation is very useful for this purpose. I will review the work of McDuff and Tolman on the Seidel representation and explain how this can be used to find an obstruction to embedding.

- Speaker
- Jongmyeong Kim (IBS-CGP)
- Title
- On a categorification of the Gromov—Yomdin theorem
- Abstract
- A topological dynamical system consists of a topological space X and a continuous self-map f on it. The topological entropy is a quantity that measures the complexity of a topological dynamical system. In general, it is hard to compute but if X is a compact Kähler manifold and f is a holomorphic automorphism, it can be computed using a linear algebraic method. More precisely, in such a case, Gromov and Yomdin showed that the topological entropy of f coincides with the spectral radius of the linear map on the cohomology induced by f. On the other hand, a categorical dynamical system, which was introduced as an analogue of a topological dynamical system, consists of a triangulated category and an exact endofunctor on it. There is also the notion of the categorical entropy. Therefore it is natural to ask how to formulate a categorical version of the Gromov—Yomdin theorem. In this talk, I will discuss about how to do that. The main ingredient is to define the “holomorphicity” of an autoequivalence using Bridgeland stability conditions. This talk is based on a joint work with Federico Barbacovi.

- Speaker
- Joontae Kim (KIAS)
- Title
- Topology of Lagrangians, and all that
- Abstract
- The study and classification of Lagrangian submanifolds in symplectic manifolds is a central topic of modern symplectic topology. In particular, we focus on the Lagrangian knot problem asking whether two given Lagrangians are isotopic. We explore how symplectic topology has been grown up together with the knowledge of Lagrangians.

- Speaker
- Sangjin Lee (IBS-CGP)
- Title
- Wrapped Fukaya category of the cotangent bundle of the torus
- Abstract
- In their famous series of papers, Ganatra-Pardon-Shende answered a basic question in sympletic topology "how could we compute Fukaya categories?". However, sometimes their result does not seem practical, since it is not easy to take homotopy colimit. In joint work with Doganca Karabas, we develop a way to resolve the difficulty of taking homotopy colimit. In this talk, I will explain the way with an example case, the wrapped Fukaya category of the cotangent bundle of the 2 dimensional torus.

- Speaker
- Sangwook Lee (Soongsil University)
- Title
- Algebraic structures behind Lagrangian submanifolds
- Abstract
- We investigate various algebraic structures of Hochschild invariants of categories which are involved in mirror symmetry. No prior knowledge is assumed.

## Accommodation

#### Room Rate (per night)

- Standard Double
- KRW 140,000
- Standard Twin
- KRW 140,000

* Breakfast(KRW 22,000) is included.

## 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), No. 2020R1A2C1A01003201 (중견연구)
- National Research Foundation of Korea(NRF), No. 2020R1C1C1A01010972 (신진연구)