• Venue: 부산 영도 라발스호텔, petit ballroom

• Date: 2025.06.30 - 2025.07.01

Schedule & Talk information

• 좌동욱 : HKR and HRR theorem for graded matrix factorization.

Abstract: In this talk, I will explain a concept of differential graded category of graded matrix factorizations. In some good cases, this DG category behaves as if it is a space; it has a notion of its own cohomology theory, Chern character, and a Riemann-Roch formula. Such abstract invariants and formulas can be written in terms of twisted deRham complex via Hochschild-Kostant-Rosenberg isomorphisms. This talk is based on joint works with B. Kim and B. Sreedhar.

• 박경동 : Deformation rigidity of smooth projective symmetric varieties of Picard number one

Abstract: Symmetric varieties are normal equivarient embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. By using the Luna-Vust theory on spherical varieties, Ruzzi classified the smooth projective symmetric varieties of Picard number one from the classification of involutions on semisimple algebraic groups and combinatorial objects called colored fans. As a result, we know that there are only six nonhomogeneous smooth projective symmetric varieties of Picard number one. In this talk, I will present results on the rigidity of smooth projective symmetric varieties of Picard number one under Kähler deformations, and discuss the remaining problems. This talk is based on joint works with Shin-young Kim.

• 박진형 : Tangent cones to secant varieties of curves

Abstract : Consider the secant varieties of smooth projective curves embedded by the complete linear systems of line bundles of sufficiently large degree. The classical Terracini lemma computes the tangent spaces to the secant varieties of curves at smooth points, but this does not say anything about local structures around singular points. In this talk, I'll explain how to calculate the tangent cones to the secant varieties of curves at singular points using resolutions of singularities and the formal function theorem. This is joint work with Lawrence Ein and Wenbo Niu.

• 이상현 : Moduli space of quasisections to relative moduli of coherent sheaves and application to Vafa-Witten invariants

Abstract: In this talk, we will introduce moduli space of quasisections to a relative moduli space of coherent sheaves over fibration X -> C, over a curve C. This is a generalization of Nesterov's theory of quasimaps to moduli space of coherent sheaves. Especially, when X -> C is a elliptic fibration from an elliptic surface X which admits nodal singularity on special fibers, we will explain how to apply the theory of quasisections to compute Vafa-Witten invariants of X. The contents of the talk is based on an ongoing project with Yaoxiong Wen.

• 조용화 : Some properties of non-isomorphic locus of linear projections

Abstract: We consider a double point divisor from outer projection, which is characterized by its support as the non-isomorphic locus of the projection. For outer projections, Mumford and Ilic studied the positivity properties (such as base point freeness and ampleness) of these divisors. I will briefly recall their results and share our recent joint work with Jinhyung Park on very ampleness of these divisors.

• 김유식 : Cluster algebras and Newton–Okounkov bodies

Abstract: Cluster algebras, introduced by Fomin and Zelevinsky, are a class of Z-subalgebras of a rational function field with a special combinatorial structure. These algebras are classified in several types: finite vs infinite type, and finite vs infinite mutation type. In this talk, we will first provide an introduction to the theory of cluster algebras and their types.
We will then explain how to distinguish Newton–Okounkov bodies constructed from cluster algebras.

Organizers: 김민훈, 김영락, 김준태, 원준영, 이재혁, 임우남, 조창연, 최성락, 홍한솔 교수님

Support staff: 최현주 (연세대 BK 행정지원)

Sponsors: 신촌 3대학원 공동세미나 지원금, 포스코청암재단, BK21 연세대학교 수리과학 및 계산 교육연구단, 삼성미래육성사업 연구비

Contact: woonamlim@yonsei.ac.kr