Tokyo-Seoul Conference in Mathematics 2025

Enumerative Geometry and Representation Theory

Invited Speakers (alphabetical order)

Sarunas Kaubrys (Kavli IPMU)

Kyoung-Seog Lee (Postech)

Woonam Lim (Yonsei University)

Kota Murakami (Kyoto University)

Anya Nordskova (Kavli IPMU)

Jeongseok Oh (Seoul National University)

Hyeonjun Park (KIAS)

Shunya Saito (University of Tokyo)

Registration

https://forms.gle/8mWpkFwqU2TDorsD9

Schedule (tentative) 

December 12 (Fri)

10:00-11:00  Hyeonjun Park

11:30-12:30  Sarunas Kaubrys

14:30-15:30  Kyoung-Seog Lee

16:00-17:00  Shunya Saito

December 13 (Sat)

10:00-11:00   Kota Murakami

11:30-12:30   Woonam Lim

14:30-15:30   Anya Nordskova

16:00-17:00   JeongSeok Oh

Titles and Abstracts

Speaker: Hyeonjun Park

Title: Symplectic pushforwards and Lagrangian classes

Abstract: In the first half of the talk, I will introduce a general operation of producing shifted symplectic stacks from given ones. Basic examples like cotangent bundles, critical loci, and Hamiltonian reduction can be understood as special cases of this operation. Moreover, this unification enables us to provide an etale local structure theorem for shifted symplectic Artin stacks.

　In the second half of the talk, I will provide a generalization of virtual classes that can be used to define following enumerative invariants: (1) cohomological field theories for gauged linear sigma models; (2) cohomological Hall algebras for 3-Calabi-Yau categories; (3) relative Donaldson-Thomas invariants for Fano 4-folds with anti-canonical divisors; (4) refined surface counting invariants for Calabi-Yau 4-folds. This is joint work in progress with Adeel Khan, Tasuki Kinjo, and Pavel Safronov.

Speaker: Sarunas Kaubrys

Title: Joyce vertex algebras with potential 

Abstract: Joyce has defined a structure of (co)vertex algebra on the (co)homology of the moduli of objects of an abelian or derived category. I will recall this construction and explain how we can extend this construction to define a covertex algebra on the critical cohomology of a quiver with potential. I will then explain how this structure is related to the localised coproduct of Davison and explain how the covertex structure is compatible with the Cohomological Hall Algebra structure. If time permits, I will explain two applications, one to cohomological integrality for symmetric quivers and one to deformed Drinfeld coproducts on Yangians of ADE type. This is joint work in progress with Alexei Latyntsev and Shivang Jindal.

Speaker: Kyoung-Seog Lee

Title: Ulrich bundles and curves on minimal Fano 3-folds

Abstract: Ulrich bundles form an interesting class of vector bundles on projective varieties. Since they were introduced by Eisenbud and Schreyer, there have been intensive works studying these bundles from various aspects. Especially, Ulrich bundles on Fano 3-folds are drawing a lot of attention these days. It turns out that studying Ulrich bundles on a Fano 3-fold is also closely related to the geometry of curves on it. In this talk, I will discuss Ulrich bundles and curves on some minimal Fano 3-folds via representations of quivers. The last part of this talk is based on several joint works in progress with Woohyuck Choi and Kyeong-Dong Park.

Speaker: Woonam Lim

Title: Chern filtration of moduli spaces of sheaves

Abstract: The cohomology ring of moduli spaces of sheaves has been a central topic in enumerative geometry due to its rich additional structures, such as tautological generators and relations, Hall algebra, perverse filtration, etc. In this talk, I will introduce a relatively new structure, called the Chern filtration, and explain why it is interesting and how it interacts with existing structures. The main focus will be on moduli spaces of one-dimensional sheaves on surfaces and moduli spaces of bundles on curves. This is based on joint works with Y. Kononov, M. Moreira, W. Pi.

Organizing committee  (alphabetical order)

Osamu Iyama (University of Tokyo)

Young-Hoon Kiem (KIAS)

Yukinobu Toda (Kavli IPMU)

Organized by

Graduate School of Mathematical Sciences, The University of Tokyo 

and KIAS

Supported by

Inamori Research Institute for Science