Workshop for Contact and Symplectic Geometry

A special event of WYSG series in Korea

June 29–July 5, 2025

North Carolina State University, North Carolina, United States

National Research Foundation of Korea

Aim and Scope

This workshop is a special event in the Workshop of Young Symplectic Geometers (WYSG) series, which has been held nine times in Korea since 2021. The series aims to share recent progress and foster collaboration among Korean researchers in contact and symplectic geometry and topology, particularly those in the early stages of their careers.

The goal of this special event is not only to carry forward the mission of the WYSG series but also to introduce fundamental concepts, recent results, and open problems to a broader audience, including graduate students at NCSU. The scope of the event includes, but is not limited to, contact and symplectic geometry and topology, as well as related topics in combinatorics, algebra, and low-dimensional topology such as cluster algebras, Legendrian knots and links, and more.

The program consists of six sessions, each featuring two consecutive 50-minute talks by invited speakers. In addition, there will be two series of 15-minute presentations by voluntary participants, referred to as WCSG Shorts.

Venue

#4201, SAS Hall
Department of Mathematics, North Carolina State University, North Carolina, United States

Talk Schedule

	June 29 (Sun)	June 30 (Mon)	July 1 (Tue)	July 2 (Wed)	July 3 (Thu)	July 4 (Fri)	July 5 (Sat)
09:50 – 10:00		Opening Remark					Departure
10:00 – 10:50		Y. Bae 1	Y. Kim 1	Slot 5-1	J. Kim 1	Free Discussion at Hunt Library
10:50 – 11:10		Break		Break
11:10 – 12:00		Y. Bae 2	Y. Kim 2	Slot 5-2	J. Kim 2
12:00 – 14:00		Lunch	Group Photo (12:00–12:10) Lunch	Lunch	Closing Remark (12:00–12:10) Lunch
14:00 – 14:50	Arrival	B. An 1	Y. Cho 1	WCSG Shorts 1	Free Discussion
14:50 – 15:10		Break		Break
15:10 – 16:00		B. An 2	Y. Cho 2	WCSG Shorts 2
16:00 – 18:00		Free Discussion
18:00 –			Workshop Dinner	Workshop Dinner

* The schedule may vary.

Online Participation

The zoom link for online participation will be provided soon.

Title & Abstract

Abstracts

Speaker: Byung Hee An (Kyungpook National University)
Title: Hilbert polynomials of configuration spaces
Abstract: The $k$-configuration space $B_k\Gamma$ of a topological space $\Gamma$ is the space of sets of $k$ distinct points in $\Gamma$. In this paper, we consider the case where $\Gamma$ is a graph of circumference at most $1$. We show that for all $k\ge0$, the $i$-th Betti number of $B_k\Gamma$ is given by a polynomial $P_\Gamma^i(k)$ in $k$, called the Hilbert polynomial of $\Gamma$. We find an expression for the Hilbert polynomial $P_\Gamma^i(k)$ in terms of those coming from the canonical $1$-bridge decomposition of $\Gamma$. We also give a combinatorial description of the coefficients of $P_\Gamma^i(k)$.

Speaker: Youngjin Bae (Incheon National University)
Title: Monotone Lagrangian Tori and Exact Lagrangian Fillings
Abstract: Monotone Lagrangian submanifolds play a central role in the study of closed symplectic manifolds, particularly in the contexts of mirror symmetry and cluster algebras. On the other hand, exact Lagrangian fillings of Legendrian submanifolds serve as important objects in the study of Weinstein manifolds. In this talk, we explore a correspondence between monotone Lagrangian tori and exact Lagrangian fillings by examining smoothed divisor complements of toric 4-manifolds. This is a joint project with Orsola Capovilla-Searle.

Speaker: Yunhyung Cho (Sungkyunkwan University)
Title: Cluster-type structure on Fano simplices and T-singularities
Abstract: A combinatorial mutation of a lattice polytope is a procedure producing a new lattice polytope and it is a combinatorial counterpart of a mutation of Landau-Ginzburg mirrors on a Fano manifold. In this talk, we will describe a certain cluster-type structure of a Fano simplex, which is the polar dual of a moment polytope of a fake weighted projective space. More precisely, we define a mutable facet of a Fano simplex and prove that the number of mutable facets (called the rank) are invariant under combinatorial mutation. Consequently, each Fano simplex gives rise to a certain rank-valent graph whose vertices and edges correspond to Fano simplices and mutations, respectively. In dimension two, we will show that a Fano triangle is of full rank (i.e., three) if and only if the corresponding fake weighted projective plane admits only T-singularities.

Speaker: Jangsoo Kim (Sungkyunkwan University)
Title: Refinement of Hikita's e-positivity theorem via Abreu--Nigro's g-functions and restricted modular law
Abstract: In this talk, we study the symmetric functions $ g_{m,k}(x;q) $, introduced by Abreu and Nigro for a Hessenberg function $ m $ and a positive integer $ k $, which refine the chromatic symmetric function. Building on Hikita's recent breakthrough on the Stanley--Stembridge conjecture, we prove the $ e $-positivity of $ g_{m,k}(x;1) $, refining Hikita's result. We also provide a Schur expansion of the sum $ \sum_{k=1}^n e_k(x) g_{m,n-k}(x;q) $ in terms of $ P $-tableaux with 1 in the upper-left corner. We introduce a restricted version of the modular law as our main tool. Then, we show that any function satisfying the restricted modular law is determined by its values on disjoint unions of path graphs. This is joint work with JiSun Huh, Byung-Hak Hwang, Donghyun Kim, and Jaeseong Oh.

Speaker: Yoosik Kim (Pusan National University)
Title: Disk Counting via GIT Quotients
Abstract: According to the Kempf–Ness theorem, the GIT quotient is equivalent to the symplectic reduction. Using this correspondence, we explain how to relate the counting of holomorphic disks between a symplectic manifold equipped with a Hamiltonian group action and its symplectic reduction. As an application, we derive the disk potential function for weight varieties obtained as quotients by the maximal torus of partial flag varieties. We also demonstrate how the disk counting depends on the choice of stability conditions.

Accommodation Suggestion

NCSU Guesthouse

1 bedroom apartment rate is USD55, and 2 bedroom apartment rate is USD65 per night.
Minimum 5 nights are required.
Breakfast is not included.
Need a reservation, contact Byung Hee An via email.

Aloft Raleigh

The room rate varies from USD160 to USD210.
Breakfast is not included.
This is the closest to the workshop venue.

Getting to NCSU

The best option for getting NCSU from overseas is to use Raleigh-Durham International Airport (RDU).

From RDU to NCSU, please visit to NCSU transportation sites #1, #2

You may also refer here for more information including campus maps.

Financial Support

Financial support for invited speakers and overseas participants is available within a limited budget. Participants who require financial support should contact the organizer in advance.

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