2026 KIAS Algebraic Geometry Seminar Series

2 April (Thu) 4:00-5:00 PM (Room 8101, KIAS)

Sz-Sheng Wang (National Yang Ming Chiao Tung University)

Title: Quantum Extremal Transitions and Special L-Values
Abstract: An extremal transition Y ↘ X of smooth projective 3-folds consists of a crepant extremal contraction φ: Y → Ȳ with curve class ℓ ∈ NE(Y), followed by a smoothing Ȳ ⇝ X. In this talk, I will consider the Type II case that φ contracts a divisor to a point, and describe how the quantum cohomology QH(X) is obtained from QH(Y) via analytic continuation, regularization, and specialization in Qℓ. Besides roots of unity, special L-values appear in lim Qℓ whenever Ȳ admits more than one smoothing. This is joint work with Shuang-Yen Lee and Chin-Lung Wang.

9 April (Thu) 2:00-3:00 PM (HCMC Seminar Room 204, Soorim Cultural Foundation Building)

Chenjing Bu (University of Oxford)

Title: Semiorthogonal decompositions for stacks
Abstract: I will explain a joint work in progress with Tudor Pădurariu and Yukinobu Toda on a construction of semiorthogonal decompositions on derived categories of coherent sheaves on algebraic stacks. This can be seen as a categorification of Donaldson–Thomas theory, and in particular, of a decomposition theorem in cohomology obtained in an earlier joint work. I will also mention its applications to categorification of quantum groups and to the Dolbeault geometric Langlands conjecture.

To get to the venue (soorim cultural foundation), you can find the information at
http://events.kias.re.kr/h/SpringHCMCColloquium2026/?pageNo=6279

28 April (Tue) 4:00-5:00 PM (Room 8101, KIAS)

Donghyeop Lee (Yonsei University)

Title: Zero-dimensional schemes with high Castelnuovo-Mumford regularity

Abstract: The Hilbert function encodes essential information about zero-dimensional schemes, and even partial information about it can impose strong geometric constraints on the configuration of points. It is well known that small initial values of the Hilbert function, especially in degree two, force the points to lie on a curve of low degree. Motivated by this phenomenon, it is natural to investigate how other invariants arising from the Hilbert function reflect geometric properties.

In this talk, we focus on Castelnuovo–Mumford regularity of zero-dimensional schemes, which is closely related to when the Hilbert function coincides with the Hilbert polynomial. We describe the geometric configuration of a zero-dimensional scheme Γ when its regularity is close to the known upper bound ⌈(d − n − 1) / t(Γ)⌉ + 2, where t(Γ) denotes the smallest integer t such that Γ admits a (t+2)-secant t(Γ)-dimensional linear space. This is joint work with Professor Euisung Park.

28 April (Tue) 14:30-15:30 PM (Room 8101, KIAS)

Saerom Sim (DGIST AGSTA-BRL)

Title: On the Geometry of the Rank 3 Loci of Veronese Embeddings

Abstract: The decomposition of homogeneous polynomials into sums of powers is a classical problem in algebraic geometry. In this talk, we revisit established results on Waring rank and secant varieties, focusing particularly on quadratic rank. Our results provide a detailed characterization of the rank 3 loci of Veronese embeddings, for which the validity of property QR(3) has recently been fully established in all characteristics.

4 May (Mon) 2:30-3:30 PM (TBA)

Xun Yu (Tianjin University)

Title: TBA
Abstract: TBA

4 May (Mon) 4:00-5:00 PM (TBA)

Keiji Oguiso (The University of Tokyo)

Title: TBA
Abstract: TBA

Past seminars

19 March (Thur) 4:00-5:00 PM (Room 8101, KIAS)

Li Li (IBS-CCG)

Title: Vector bundle techniques in the intersection of quadrics containing a curve
Abstract: The criterion of the existence of subbundle of rank 2 vector bundle on curves was developed to solve the moduli problems of rank 2 vector bundles. Green-Lazarsfeld used such a technique to discuss the intersection of quadrics containing a curve of large degree. Later Lange-Sernesi discussed about Prym canonical curves in the similar way. In this talk, I will apply the same method to the non-complete linear system to discuss the intersection of quadrics containing a generic projected canonical curve.

27 February (Fri) 4:00-5:30 PM (Room 8101, KIAS)

Chenyang Xu (Princeton University)

Title: Properness of K-moduli
Abstract: (Joint with Harold Blum, Yuchen Liu, and Ziquan Zhuang) We present a new proof of the properness of K-moduli spaces. While our approach still depends on the higher-rank finite generation theorem, it avoids the use of Halpern-Leistner’s Θ-stratification theory. Instead, we develop a purely birational method, rooted in a relative framework for K-stability, which provides a more direct geometric proof of properness.

24 February (Tue) 4:00-5:00 PM (Room 8101, KIAS)

Minseong Kwon (Morningside Center of Mathematics, AMSS, CAS)

Title: Automorphism groups of toroidal horospherical varieties
Abstract: Toroidal horospherical varieties are equivariant toric variety bundles over rational homogeneous spaces, naturally generalizing the notion of toric varieties. In this talk, I will discuss the automorphism groups of toroidal horospherical varieties. Namely, I will present a structure theorem for the automorphism group of a smooth complete toroidal horospherical variety, which yields a combinatorial criterion for the reductivity of the automorphism group, generalizing the result of Demazure in the case of toric varieties. If time permits, as an application, I will give many examples of K-unstable Fano projective bundles over rational homogeneous spaces. This talk is based on a joint work in progress with Lorenzo Barban and DongSeon Hwang.

Organized by Yen-An Chen, Doyoung Choi, Jong In Han, Parvez Rasul, Jemin You, and Minzhe Zhu