The 9^th Workshop for Young Symplectic Geometers

December 13–15, 2024

Jeonbuk National University, Jeonju, Korea

National Research Foundation of Korea

QSMS Center for Quantum Structures in Modules and Spaces

Invited Speakers

Hyunbin Kim (Yonsei University)
Seongchan Kim (Kongju National University)
Sukjoo Lee (IBS-CGP)

Organizers

Byung Hee An (Kyungpook National University)
Youngjin Bae (Incheon National University)
Yunhyung Cho (Sungkyunkwan University)
Yoosik Kim (Pusan National University)
Myeonggi Kwon (Jeonbuk National University)

Venue

Jeonbuk National University, Jeonju, Korea

Talk Schedule

	December 13 (Fri)	December 14 (Sat)	December 15 (Sun)
10:00 – 10:30	Arrival and Registration	S. Kim (II)	H. Kim (III)
10:30 – 11:00		Question Session
11:00 – 11:30		H. Kim (II)	Lee (III)
11:30 – 12:00		Question Session	Closing Remark
12:00 – 14:00		Lunch
14:00 – 14:30		Lee (II)	Free Discussion
14:30 – 15:00	Opening Remark	Question Session
15:00 – 15:30	S. Kim (I)	S. Kim (III)
15:30 – 16:00	Question Session
16:00 – 16:30	H. Kim (I)	WYSG Shorts 1
16:30 – 17:00	Question Session
17:00 – 17:30	Lee (I)	WYSG Shorts 2
17:30 – 18:00	Question Session
18:00 -	Workshop Dinner		Departure

* The schedule may vary.

Title & Abstract

Abstracts

Speaker: Hyunbin Kim (Yonsei University)
Title: Semi-Simplicity of the Quantum Cohomology of Log Calabi-Yau Surfaces and Mirror Symmetry
Abstract: Using tropical geometry, we develop a method for precisely identifying the critical points of Landau-Ginszburg potential of a log Calabi-Yau surface. We analyze the change in the number/location of critical points of the potentials under blowups/blowdowns of log Calabi-Yau surfaces, proving that the mirror potential is a Morse function for generic parameters. Semi-simplicity of the Jacobian ideal ring then implies that the quantum cohomology of log Calabi-Yau surfaces is semi-simple, thereby establishing closed string mirror symmetry.

Speaker: Seongchan Kim (Kongju National University)
Title: Transverse folaition for three-dimensional Reeb flows
Abstract: In his pioneering work, using pseudoholomorphic curves in the symplectisations, Hofer studied Hamiltonian flows restricted to an energy level which is of contact type. He then proved many cases of Weinstein's conjecture on the existence of a periodic orbit in dimension three. The theory further developed by Hofer, Wysocki and Zehnder, and since then, pseudoholomorphic curves in symplectisations have been used as a powerful tool to study Hamiltonian systems with two degrees of freedom. In particular, they introduced a notion of a transverse foliation, which is a singular foliation of an energy level, where the singular set consists of finitely many periodic orbits, called bindings, and the regular leaves are punctured Riemann surfaces transverse to the flow and asymptotic to the bindings at the punctures. This allows one to reduce the Hamiltonian dynamics on the three-dimensional energy level to the study of an area-preserving surface map. In this lecture series, I will provide a gentle introduction on the theory of Hofer, Wysocki and Zehnder and explain how to construct transverse foliations in various concrete problems such as the restricted three-body problem. This is based on joint work with Naiara de Paulo, Umberto Hryniewicz, Pedro Salomão and Alexsandro Schneider.

Speaker

Sukjoo Lee (IBS-CGP)

Title

Fukaya Categories Related to Hypertoric Manifolds

Abstract

The goal of this talk series is to introduce a new higher-dimensional playground for symplectic geometers and to explore some conjectures and results related to Fukaya categories.

Talk 1) Introduction to (additive) hypertoric manifolds: Revisiting A_n Milnor fibration.

Talk 2) Weinstein structure of hypertoric manifolds and torus fibrations.

Talk 3) The Lekili-Segal conjecture and formality questions.

National Research Foundation of Korea(NRF)
QSMS Center for Quantum Structures in Modules and Spaces

The 9th Workshop for Young Symplectic Geometers