2026 KIAS Algebraic Geometry Seminar Series

8 July (Wed) 2:30-3:30 PM (HCMC Seminar Room 204, Soorim Cultural Foundation Building)

Changho Han (Korea University)

Title: Computing degenerations of K3 surfaces via Tschirnhausen bundles
Abstract: A K3 surface with a nonsymplectic automorphism of order 3 is a triple cover of a rational surface. The moduli space of such K3 surfaces admits several compactifications — Baily-Borel, toroidal, and KSBA — whose boundary strata parameterizes datas coming from limiting mixed Hodge structures. But what do the boundary surfaces actually look like? I will explain how to explicitly construct degenerations of those K3 surfaces via the Tschirnhausen bundle of triple covers of nodal rational curves. This talk is based on several joint works with Valery Alexeev, Anand Deopurkar, and Philip Engel.

8 July (Wed) 4:00-5:00 PM (HCMC Seminar Room 204, Soorim Cultural Foundation Building)

Sung Rak Choi (Yonsei University)

Title: On the Morrison-Kawamata dream space and its applications
Abstract: I will introduce the notion of Morrison-Kawamata dream spaces which axiomatizes the varieties that satisfy the Morrison-Kawamata cone conjecture. I will also discuss the basic theory and some properties of MKD spaces. 

20 August (Thu) 2:30-3:30 PM (TBA)

Min-Gyo Jeong (Sungkyunkwan University)

Title: TBA
Abstract: TBA

20 August (Thu) 4:00-5:00 PM (TBA)

Dongsoo Shin (Chungnam National University)

Title: Relative Equisingular Deformation Theory under Resolution Subgraph Surgery

Abstract: This talk develops a relative approach to equisingular deformation theory for rational surface singularities, viewed through surgery operations on connected subgraphs of a resolution graph. The central problem is to compare the logarithmic tangent cohomology $H^1(V,T_V(-\log{E}))$ before and after removing or attaching a terminal linear chain, with the aim of obtaining effective estimates for $h^1(V,T_V(-\log{E}))$. In the terminal-linear-chain case, we describe how the self-intersection data, the infinitesimal motion of the attaching points, and the analytic gluing contribution are reflected in the resulting variation of logarithmic cohomology. This relative viewpoint is intended to separate the graph-theoretic contribution from the analytic-moduli-dependent contribution, thereby providing a deformation-theoretic calculus along the resolution graph. As applications, we discuss possible implications of these \(h^1\)-estimates for Wahl's Rational Conjecture, the classification of rational surface singularities admitting rational homology disk smoothings, and related questions in the deformation theory of surface singularities; part of this work in progress is joint with Márton Beke, Heesang Park, András Stipsicz.

TBA

Yeongrak Kim (Pusan ​​National University)

Title: TBA
Abstract: TBA

22 October (Thur) 4:00-5:00 PM (Room 8101, KIAS)

Jihun Park (POSTECH)

Title: TBA
Abstract: TBA

Past seminars

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.

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.

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.

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) 2:30-3:30 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.

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.

4 May (Mon) 2:30-3:30 PM (Room 8101, KIAS)

Xun Yu (Tianjin University)

Title: Nonrational varieties with unirational parametrizations of coprime degrees

Abstract: We show that there exists a 2-dimensional family of smooth cubic threefolds admitting unirational parametrizations of coprime degrees. This together with Clemens-Griffiths' work solves the long standing open problem whether there exists a nonrational variety with unirational parametrizations of coprime degrees. Our proof uses a new approach, called the Noether-Cremona method, for determining the rationality of quotients of hypersurfaces. This is a joint work with Song Yang and Zigang Zhu.

4 May (Mon) 4:00-5:00 PM (Room 8101, KIAS)

Keiji Oguiso (The University of Tokyo)

Title: Algebraic dynamics of Calabi-Yau manifolds of Wehler type

Abstract: A general hypersurface $X$ of multi-degree 2 in $(\P^1)^{d+1}$ is called a Calabi-Yau manifold of Wehler type (of dimension $d >2$). In this talk, after recalling some remarkable properties of $X$ found by Cantat and me, I would like to show that $X$ has a birational primitive automorphism, in particular, a birational automorphism with Zariski dense orbit, in any dimension $d > 2$. This is a generalization of my earlier work with some corrections of proof there. 

11 June (Thur) 4:00-5:00 PM (Room 1424, KIAS)

Jinhyung Park (KAIST)

Title: Ulrich sheaves and determinantal representations on higher secant varieties of curves

Abstract: We show that higher secant varieties of smooth projective complex curves have symmetric admissible determinantal representations with symmetric Ulrich sheaves of rank one under some mild conditions on the embedding line bundles of the curves. We employ cohomological computations on symmetric products of curves and higher Szegő kernels associated to non-effective theta characteristics. This is joint work with Daniele Agostini and Mario Kummer. 

Organized by Yen-An Chen, Doyoung Choi, Jong In Han, Parvez Rasul, Jemin You, and Minzhe Zhu with the faculty advisor Young-Hoon Kiem