Workshop for
Young Symplectic Geometers

June 18–20, 2021

Kyungpook National University, Daegu, Korea

Invited Speakers

Click here for the KNU campus map.

* We will provide daily parking tickets to those who bring their cars.

	June 18 (Fri)	June 19 (Sat)	June 20 (Sun)
10:00 – 10:30		Dongwook Choa	Jongmyeong Kim
10:30 – 11:00		Question Session
11:00 – 11:30		Yoosik Kim	Sangjin Lee
11:30 – 12:00		Question Session	Closing Remark
12:00 – 14:00		Lunch
14:00 – 15:00	Arrival and Registration	Free Discussion & Question Session	Departure
15:00 – 15:15	Arrival and Registration
15:15 – 15:30	Opening Remark
15:30 – 16:00	Hansol Hong
16:00 – 16:30	Question Session
16:30 – 17:00	Taekgyu Hwang
17:00 – 17:30	Question Session
17:30 – 18:00	Donghoon Jang

* The schedule may vary.

Speaker: Dongwook Choa (KIAS)
Title: Topology of weighted homogeneous singularities and its two categorification
Abstract: A construction of any Fukaya-type category would involve a lot of foundational work, but its geometric intuitions can be surprisingly simple. In this expository talk, we will revisit century-old results concerning topologies of weighted homogeneous polynomial W. Two categories arise as there symplectic categorifications. If time permits, I will explain interesting application concerning the relation between Milnor fibers and its compactification divisor. This talk is based on the joint work with C-H. Cho and W. Jeong.

Speaker: Hansol Hong (Yonsei University)
Title: Roles of holomorphic disks in mirror symmetry
Abstract: Lagrangian Floer theory tells us that the intersection between Lagrangians can be effectively captured by studying holomorphic disks with boundaries lying on them. Furthermore, their enumeration lies at the heart of mirror construction, providing indispensable quantum information to correct a naive mirror. We will look into some algebraic deformation problem that encodes the count of holomorphic disks, and discuss related mirror symmetry questions.

Speaker: Taekgyu Hwang (Ajou University)
Title: Symplectic embeddings of balls
Abstract: I am going to review Gromov's non-squeezing theorem to see how the existence of a J-holomorphic curve obstructs a symplectic embedding of a large ball. After looking at some examples, I will describe methods of constructing embeddings of balls.

Speaker: Donghoon Jang (Pusan National University)
Title: Symplectic circle actions with isolated fixed points
Abstract: Let the circle group act symplectically on a compact connected symplectic manifold M with k fixed points. If k=1, M is a point. If k=2, M is the 2-sphere or the dimension of M is 6. If k=3, M is equivariant symplectomorphic to the complex projective space $\mathbb{CP}^2$. We discuss ideas of studying symplectic circle actions that have isolated fixed points.

Speaker: Jongmyeong Kim (IBS-CGP)
Title: Entropies in symplectic geometry
Abstract: A symplectic manifold together with a symplectomorphism form a discrete dynamical system. To study the complexity of such a dynamical system, one can use various kinds of entropies: topological entropy, Floer-theoretic entropy, categorical entropy and so on. In this talk, I will focus on the categorical entropy and also explain a conjectural relationship between the categorical and Floer-theoretic entropies. In particular, we will see how the entropy of the composition of two Dehn twists along Lagrangian spheres $L_1,L_2$ depends on the total dimension of the Floer cohomology of $L_1,L_2$. This is based on a joint work with Federico Barbacovi.

Speaker: Yoosik Kim (Pusan National University)
Title: Symplectic geometry of flag varieties
Abstract: In this talk, I will focus on the complete flag variety $Fl(1,2;3)$. After explaining its symplectic topology and mirror symmetry, I will explain generalizations of the aspects toward other partial flag varieties.

Speaker: Sangjin Lee (IBS-CGP)
Title: Dynamics in symplectic geometry
Abstract: As you can see in Jongmyeong Kim's abstract, a symplectomorphism on a symplectic manifold forms a dynamical system. In this talk, we will see why the dynamical system is interesting. We briefly review a motivational result of Thurston, which considers similar dynamics on surfaces. Then, we can see what we can expect in symplectic geometry.