• 장소: 전주 관광호텔 꽃심

• 일정: 2025.11.13 - 16

Research Talks

• 좌동욱 (충북대학교)

• 임우남 (연세대학교)

• 이동건 (IBS-CCG)

• 이상현 (아주대학교)

• 오정석 (서울대학교)

• 박현준 (KIAS)

• 유제민 (서울대학교)

Contributed Talks

• 김준혁 (서울대학교)

• 윤득재 (서울대학교)

• 윤승재 (서울대학교)

• 이준한 (연세대학교)

• 이중민 (연세대학교)

• 한우진 (서울대학교)

Schedule

Schedule

• 오정석 - Enumerative problems

Abstract: I would like to overview two different projects working in progress, one with Dongwook Choa, Richard Thomas; and the other with Y.P. Lee, Seungjae Yun. They are about K-theoretic Lagrangian classes/pullbacks which will be explained a bit more by Dongwook Choa; and about the blowup conjecture which will be explained more by Seungjae Yun. 

• 좌동욱 - Specializing matrix factorisations

Abstract: I will explain the notion of matrix factorisation, why it is important, and how it can be specialised under certain circumstances. I will also explain how the specialization led us to construct a K-theoretic pull-back from a (-1)-symplectic derived scheme to a (-1)-Lagrangian. This is a joint work with Jeongseok Oh and Richard Thomas.

• 윤득재 - Mirror Symmetry of Non-Split Projective Bundles

Abstract: According to Givental, mirror symmetry can be stated as finding the mirror map between the J-function and the I-function. It generalizes to the statement that the I-function lies in the Givental cone determined by the J-function. A result of Brown was that the Elezi-Brown I-function lies in the Givental cone of the projectivization of a split bundle. Recently, Iritani and Koto have developed this statement for a non-split bundle. In this talk, I will explain how the construction is done and introduce its applications.

• 이준한 - Moduli of instanton quiver representations in 2D, 3D, and 4D

Abstract: We define the moduli space of quiver representations and study the case of the 1-loop quiver, corresponding to the instanton moduli space. In the two-dimensional case, we observe that the moduli space becomes a holomorphic symplectic variety in the sense of Nakajima, and we examine its torus-fixed points. Similar torus-fixed point structures appear in the three- and four-dimensional cases. We briefly discuss the result of Arbesfeld-Kool-Lim, where the quadratic form induces a (−2)-shifted symplectic structure, and use the Oh–Thomas virtual class, localization formula to compute generating functions of Donaldson–Thomas invariants. At the end of the talk, we consider questions regarding ADHM descriptions, localization, and orientation data for arbitrary quivers.

• 이중민 - Moduli space of parabolic bundles

Abstract: Stable vector bundles on smooth projective curves and their moduli spaces have long been a central theme in algebraic geometry. Introducing parabolic structures provides a way to refine stability and incorporate local data at marked points, thereby leading to a richer structure. In studying the moduli of parabolic bundles, intersection numbers of tautological classes are fundamental invariants. Building on the work of M. Moreira, who showed that such intersection numbers are determined by certain structural properties, we aim to establish an analogue for parabolic vector bundles equipped with a symplectic form.

• 임우남 - Curious symmetry of Chern filtration of moduli space of bundles on curves

Abstract: The cohomology ring of the moduli space of bundles on curves has long been studied, leading to an almost complete understanding of its structure. This cohomology ring admits a refined structure called the Chern filtration. Numerical experiments suggest that this refinement exhibits a certain symmetry. In this talk, I will explain a conjectural curious symmetry of the Chern filtration of the moduli space of bundles on curves, motivated by the curious Hard Lefschetz symmetry of character varieties, and present results in the rank 2 case. This is joint work with M. Moreira and W. Pi.

• 박현준 - Counting surfaces via stable pairs

Abstract: I will give an introduction to surface counting invariants on Calabi-Yau 4-folds. I will mainly focus on PT1 invariants of local surfaces. 

• 이동건 - Cohomology of the Hacking moduli space of quartic plane curves

Abstract: In the early 2000s, Hacking introduced a compact moduli space of plane curves of a fixed degree. This construction provided one of the first examples of compact moduli spaces of higher-dimensional pairs, generalizing the moduli spaces of pointed (rational) curves. Despite its significance, the cohomology of this space has remained largely unexplored. Recent developments in moduli theory provide a way to relate the Hacking moduli space to its GIT model via wall crossings of stability conditions. Building on these ideas, we compute the cohomology of the moduli space in the case of plane quartics. This is joint work in progress with Kenneth Ascher.

• 유제민 - Local geometry of 0-shifted symplectic moduli stacks

Abstract: Many moduli spaces that appear in algebraic and enumerative geometry are singular, but behave “as if” they were symplectic. A fundamental example is the moduli stack of sheaves on a K3 surface: the stable locus is a smooth symplectic variety via Mukai’s form, but the full stack is singular. The framework of 0-shifted symplectic structures extends this symplectic geometry to the derived enhancements of such singular moduli stacks. In this talk, I will explain a local structure theorem for 0-shifted symplectic derived Artin stacks. Roughly, such a derived stack is formally locally a Hamiltonian reduction of a symplectic formal scheme. I will also discuss how such local models can be used to analyze the singularities of moduli of sheaves on K3 surfaces near strictly semistable points. This is joint work in progress with Young-Hoon Kiem and Hyeonjun Park.

• 이상현 - Euler characteristic of moduli space of symplectic(or orthogonal) bundles over toric surfaces

Abstract: Klyachko classified equivariant vector bundles over toric varieties. He described equivariant vector bundles in terms of discrete data and elements in product of Grassmannians. Using this, Kool related GIT stability of the product of Grassmannian via GL(r)-action and stability of vector bundles, furthermore he described torus fixed locus of the moduli space of sheaves in terms of these GIT quotients. As an application, he computed Euler characterics of moduli space of slope stable sheaves over smooth projective toric surfaces. Recently, Kavesh and Manon generalized Klyachko's classification for equivariant G-bundles. Using this, we describe torus fixed locus of moduli space of G-sheaves when G=Sp_2n, O_r, SO_r, and moreover we describe their torus fixed locus in terms of GIT quotient of isotropic Grassmannians via G-action. We also compute some Euler characteristic of these moduli space when the base space is a smooth projective toric surface, such as P^2.

• 김준혁 - Quantum-classical reduction and its applications

Abstract: In 2003, Buch, Kresch and Tamvakis showed that any three-pointed, genus 0 Gromov-Witten invariants on Grassmannians can be computed as a classical triple intersection of certain partial flag varieties, hence reducing the quantum cohomology of Grassmannians to the classical cohomology of flag varieties. In this talk, I will explain their construction and related concepts.

• 한우진 - Oh-Thomas virtual fundamental class in DT4 theory

Abstract: I will explain the Oh-Thomas algebraic construction of algebraic virtual cycles for moduli of coherent sheaves on Calabi-Yau 4-folds. The construction produces an algebraic virtual fundamental class by localizing Edidin-Graham's square root Euler class for SO(r,C)-bundles to zero locus of an isotropic section. The resulting virtual fundamental class admits torus localization, enabling computations of DT4 invariants.

• 윤승재 - Non-vanishing and vanishing of quantum blowups

Abstract: It is known that a quasi-smooth morphism of DM stacks satisfies the so-called "pushforward property" between virtual cycles. The blowup being regarded as the first non-trivial example outside of this quasi-smooth case, it was conjectured initially by Y.P. Lee that the pushforward property still holds in the blowup setting. In this talk. I will share some recent ideas regarding this blowup conjecture. This is a joint work in progress with Y.P. Lee and Jeongseok Oh.

Organizers: Woonam Lim, Jeongseok Oh, Hyeonjun Park

Contact: woonamlim@yonsei.ac.kr