Center for Complex Geometry

Enriques surfaces of zero entropy
2025-12-15 16:30 - 17:30 (Asia/Seoul) | B236-1, IBS, Korea, Republic of
Speaker

Gebhard Martin
University of Bonn

The automorphism group of a general Enriques surface is the 2-congruence subgroup of the Weyl group of the E10-lattice. In particular, it is infinite and not virtually solvable. On the other end of the spectrum, there do exist Enriques surfaces with finite automorphism group, first classified over the complex numbers by Nikulin and Kondo. In this talk, I will explain the classification of Enriques surfaces with infinite and virtually Abelian automorphism group. This is joint work with Giacomo Mezzedimi and Davide Veniani.

Kyoung-Seog Lee, On intersection of two quadrics I
2025-12-29 16:00 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Kyoung-Seog Lee
POSTECH

Intersections of two quadrics form an interesting class of algebraic varieties and they have been intensively studied from various aspects. In these talks, I will discuss these various aspects of the intersection of two quadrics and how to interpret/generalize some of the classical algebraic geometry results using the derived category of coherent sheaves. The last part of these talks is based on a joint work in progress with Jiwan Jung and Han-Bom Moon.

Kyoung-Seog Lee, On intersection of two quadrics II
2025-12-30 11:00 - 12:30 | B236-1, IBS, Korea, Republic of

Torsion points on holomorphic sections of elliptic surfaces
2026-01-21 15:00 - 16:00 | B236-1, IBS, Korea, Republic of
Speaker

Sui-Chung Ng
ECNU

A complex algebraic surface is called an elliptic surface if it is a fiber surface whose general fibers are elliptic curves. An elliptic surface can also be regarded as an elliptic curve $E$ over the function field $K$ of an algebraic curve. The holomorphic sections of that elliptic surface can then be regarded as $K$-rational points of $E$. In the 90s, N. Mok proposed and started to use differential geometry to study these $K$-rational points (as holomorphic sections). In this talk, we will discuss how to study the torsions points on such holomorphic sections within this framework. This is based on a joint work with N. Mok.

On the rank of Hermitian polynomials and the SOS Conjecture
2026-01-21 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Yun Gao
Shanghai Jiao Tong U

Hilbert’s 17-th problem asked whether a non-negative polynomial in several real variables must be a sum of squares of rational functions. There is also a quantitative version of Hilbert’s 17th problem which asks how many squares are needed. D’Angelo extend this problem to more general case which is called Hermitian or complex variable analogues of Hilbert’s problem. Let $zinmathbb C^n$ and $|z|$ be its Euclidean norm. Ebenfelt proposed a conjecture regarding the possible ranks of the Hermitian polynomials in $z,bar z$ of the form $A(z,bar z)|z|^2$, known as the SOS Conjecture, where SOS stands for “sums of squares”. In this talk, we will introduce a dimension formula for local holomorphic mappings. As an application, we use this formula to study this conjecture and its generalizations to arbitrary signatures for a Hermition forms on $mathbb C^n$. It is joint work with Sui-Chung Ng.

On Slope Unstable Fano varieties
2026-02-26 16:00 - 17:00 | B236, IBS, Korea, Republic of
Speaker

Yen-An Chen
KIAS

For Fano varieties, significant progress has been made recently in the study of K-stability, while the understanding of the weaker but more algebraic concept of $(−K)$-slope stability remains intricate. For instance, a conjecture attributed to Iskovskikh states that the tangent bundle of a Picard rank one Fano manifold is slope stable. Peternell-Wisniewski and Hwang proved this conjecture up to dimension five in 1998, but Kanemitsu later disproved it in 2021. To address this gap in understanding, we present a method that aims to characterize the geometry associated with the maximal destabilizing sheaf of the tangent sheaf of a Fano variety. This approach utilizes modern advancements in the foliated minimal model program. In dimension two, our approach leads to a complete classification of $(−K)$-slope unstable weak del Pezzo surfaces with canonical singularities. As by-products, we provide the first conceptual proof that $mathbb{P}^1 times mathbb{P}^1$ and $mathbb{F}_1$ are the only $(−K)$-slope unstable nonsingular del Pezzo surfaces, recovering a classical result of Fahlaoui in 1989. This is the joint work with Ching-Jui Lai.

On the virtual cohomological dimensions of automorphism groups of K3 surfaces
2026-02-27 16:30 - 17:30 | B236, IBS, Korea, Republic of
Speaker

Taiki Takatsu
Tokyo University of Science

We will discuss Mukai’s conjecture that the virtual cohomological dimension of the automorphism group of a K3 surface is equal to the maximum rank of its Mordell-Weil groups. The action of the automorphism group on the second cohomology induces a natural action on a hyperbolic space. In this talk, we will explain that Mukai’s conjecture can be regarded as a problem in hyperbolic geometry and geometric group theory via this action. In particular, we give the formula that determines the virtual cohomological dimension of the automorphism group of a K3 surface by the covering dimension of the blown-up boundary associated with the ample cone of the K3 surface. If time permits, we will give an affirmative example and a counterexample of Mukai’s conjecture.

Cone structures and conic connections
2026-03-04 16:00 - 17:00 | B236, IBS, Korea, Republic of
Speaker

Katharina Neusser
Masaryk University

A cone structure on a manifold $M$ is given by a closed submanifold $mathcal Csubset mathbb P TM$ of the projectived tangent bundle of $M$, which is submersive over $M$. Such geometric structures arise naturally in differential and algebraic geometry and they come often equipped with a conic connection, which specifies a distinguished family of curves on $M$ in directions of $mathcal C$. In a joint work with Jun-Muk Hwang we defined an important local invariant for so-called characteristic conic connections, namely the cubic torsion. In this talk I will give a geometric interpretation of the cubic torsion and will discuss some applications. This talk is based on joint work in progress with Andreas Čap.

Workshop on Birational Geometry, Moduli, and Syzygy
2026-03-10 - 2026-03-13 | B109, IBS, Korea, Republic of
Speakers
Invited Lecturers (three one-hour lectures)
Dawei Chen (Boston College)
Gavril Farkas (Humboldt University of Berlin)
Francesco Russo (University of Catania)
Invited Speakers (one-hour talk)
Minyoung Jeon (IBS-CCG)
Donggun Lee (KIAS)
Li Li (IBS-CCG)
Abstracts
PDF file
Schedule

Mar 10 (Tue)
Mar 11 (Wed)
Mar 12 (Thu)
Mar 13 (Fri)

10:00~11:00

Russo, Lec 1
Russo, Lec 2
Russo, Lec 3

11:30~12:30

Chen, Lec 1
Chen, Lec 2
Chen, Lec 3

12:30~14:30
Registration
(begins at 14:00)
Lunch & Discussion
Lunch & Discussion
Lunch & Discussion

14:30~15:30
Farkas, Lec 1
Farkas, Lec 2
Farkas, Lec 3

16:00~17:00
Li
Jeon
Lee

17:30~19:30
Dinner for Speakers
Banquet
Dinner for Speakers

(There will be a coffee/tea break between talks each day.)
Organizers
Yongnam Lee (IBS-CCG)
Jinhyung Park (KAIST)
Venue
B109, IBS, Daejeon, Korea
Registration
Please submit Google form by February 20.
Main Hotel
Lotte City Hotel Daejeon (4-30 Doryong-dong, Yuseong-gu, Daejeon)
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Cylindricity of weighted singular del Pezzo surfaces defined over fields of characteristic zero
2026-04-02 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Dae-Won Lee
Ewha Womans University

The study of cylinders in normal projective varieties is of significant interest due to their intrinsic link to unipotent group actions on affine algebraic varieties. Over a field $mathbb{k}$ of characteristic zero, it is known that cylindricity in lower-dimensional varieties (appearing as generic fibers) implies the existence of vertical cylinders in higher-dimensional fibered spaces. In this talk, we give a criterion for the cylindricity of $mathbb{k}$-forms of a singular del Pezzo surface obtained as a blow-up of a weighted projective plane. Moreover, using the aforementioned criterion, we construct a Fano 3-fold which contains a vertical cylinder. This is joint work with In-Kyun Kim and Masatomo Sawahara.

Anticanonical minimal model program: examples and applications
2026-04-03 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Dae-Won Lee
Ewha Womans University

This talk provides a brief survey of recent results and applications concerning the anticanonical minimal model program. Furthermore, we present examples of varieties that admit an anticanonical minimal model despite not being Mori dream spaces. This talk is based on joint work with Sung Rak Choi, Sungwook Jang and Donghyeon Kim.

Seminar week on Moduli, Birational Geometry, and related topics
2026-05-27 - 2026-05-29 | B236-1, IBS, Korea, Republic of
Speakers
Shigeyuki Kondo (Nagoya University)
JongHae Keum (KIAS)
Fei Si (Xi’an Jiaotong University)
Kyoung-Seog Lee (POSTECH)
Sang-Bum Yoo (Gongju National University of Education)
Junchao Shentu (USTC)
Haesong Seo (IBS-CCG/KAIST)
Minzhe Zhu (KIAS)
Yen-An Chen (KIAS)
Abstracts
PDF file
Schedule
May 27(Wed)
15:00-16:00, Shigeyuki Kondo
16:30-17:30, JongHae Keum
May 28(Thu)
11:00-12:00, Fei Si
13:30-14:30, Kyoung-Seog Lee
15:00-16:00, Sang-Bum Yoo
16:30-17:30, Junchao Shentu
May 29(Fri)
10:00-11:00, Haesong Seo
11:20-12:20, Minzhe Zhu
14:00-15:00, Yen-An Chen
Organizers
Yongnam Lee (IBS-CCG)
Venue
B236-1, IBS, Daejeon, Korea
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Morse-Bott functions from complex structures
2026-05-27 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Hyunmoon Kim
Ewha Womans University

We present a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. Its stable manifolds generalize the Lagrangian, symplectic, isotropic, and coisotropic Grassmannians to include the Grassmannians of linear subspaces that are neither isotropic, coisotropic, nor symplectic. The negative gradient flow deformation retracts these stable manifolds to compact homogeneous spaces for the unitary group.

Some geometric problems on G-varieties of complexity 1
2026-06-16 16:00 - 17:00, 2026-06-17 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Yan Li
Beijing Institute of Technology

Let $G$ be a connected, reductive, linear algebraic group that acts on a normal variety $X$, and $B$ be a Borel subgroup group of $G$. The complexity of the $G$-action on $X$ was defined by E. B. Vinberg in 1985 as the codimension of $B$-orbit at a sufficiently general position. $G$-varieties of complexity 0 are the well-known spherical varieties, which have been widely studied by many authors in the past decades. $G$-varieties of complexity 1 also provides rich examples, the basic theory on geometrical structure was founded by D. A. Timashev in 1997.
In the first lecture, I will give an overview on the classification theory, as well as some fundamental theorems on geometrical structure of $G$-varieties of complexity 1 which are mainly established by D. A. Timashev. In the second one, I will introduce some recent works on geometrico-analysis problems on $G$-varieties of complexity 1, such as K-stability and its weighted version. We will start from the former works of Suss, Ilten, Langlois, Terpereau, etc. until our recent ones.

Birational contractions of (overline{mathrm{M}}_{g,n}) and their dependence on the characteristic
2026-07-01 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Daebeom Choi
University of Pennsylvania

In this talk, we discuss the existence and nonexistence of certain birational contractions of (overline{mathrm{M}}_{g,n}). Somewhat surprisingly, this depends on the characteristic of the base field: many such contractions exist only in positive characteristic. We present a precise form of this phenomenon and discuss two examples that highlight the difference between characteristic zero and positive characteristic. The first is a simple and explicit contraction that exists only in positive characteristic, and the second is a modular interpretation of the morphisms associated with psi classes on (overline{mathrm{M}}_{1,n}). We also offer some speculation on why such characteristic-dependent phenomena arise.

Mutation of Fano Simplices and Markov type equations
2026-07-03 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Yunhyung Cho
Sungkyunkwan University

It is well known that there is a bijective correspondence between the set of positive integer solutions to the Markov equation and the set of Fano triangles mutation equivalent to the Fano triangle of $mathbb{P}^2$.
In this talk, we establish a higher dimensional generalization of this correspondence for arbitrary Fano simplices of any dimension. On the polyhedral side, we introduce a distinguished class of facets, called admissible facets, and show that their number is preserved under facet mutation. As a consequence, facet mutation classes of Fano simplices carry natural exchange graph structures whose valency is equal to the number of admissible facets. On the arithmetic side, we associate to each Fano simplex a weighted Markov-type equation together with a distinguished positive integer solution, and show that the corresponding arithmetic mutations, given by Vieta involutions, are compatible with facet mutations. More precisely, the assignment from Fano simplices to Diophantine data intertwines combinatorial mutations with arithmetic mutations, thereby relating the mutation dynamics of Fano simplices to the arithmetic dynamics of positive integer solutions. Finally, we introduce a piecewise linear transformation on dual polytopes, called a sliding operator, which realizes combinatorial mutation in the dual picture. As applications, we obtain a volume formula for dual simplices in terms of the associated Diophantine data and recover the multiplicity change formula under mutation.

Indeterminacy of period map for hypersurfaces
2026-07-09 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Sung Gi Park
Princeton University

I will discuss the indeterminacy locus of the period map from the moduli space of hypersurfaces to the period domain and its compactifications. In the case of quartic K3 surfaces, the result verifies the expectation of Laza and O’Grady that the period map from the GIT compactification is regular precisely on the semi-log canonical locus.

Hodge structure on the singular cohomology of singular cubic fourfolds
2026-07-10 10:00 - 11:00 | B236-1, IBS, Korea, Republic of
Speaker

Hyunsuk Kim
University of Michigan

Considering the singular cohomology of a cubic fourfold yields a morphism from the moduli space of (smooth) cubic fourfolds to the period domain. Both spaces have natural compactifications, the GIT moduli space of cubic fourfolds parametrizing all GIT polystable objects, and the Baily-Borel compactification of the period domain, purely coming from group theory. This yields a birational map between two projective varieties. Laza and Looijenga independently gave a precise description of the birational geometry between these two spaces. Recently, Sung Gi Park gave a systematic understanding on this picture using Hodge-Du Bois theory and higher singularities, which have been developed by Friedman-Laza, Mustata-Popa, and many others.
In order to attack this question, it is vital to understand the Hodge structure on the singular cohomology of a singular member in this moduli problem, and also the Hodge theoretic properties of a degeneration to it. In a joint work with Kenny Ascher, Jennifer Li, Lisa Marquand, Sung Gi Park, and Sasha Viktorova, we systematically carry out the calculation of the Hodge-Du Bois diamond of all GIT polystable cubic fourfolds using techniques coming from Saito’s Hodge modules.

Intensive Lectures on the Algebraic Montgomery-Yang Problem
2026-08-07 - 2026-08-08 | 8101, KIAS
Speakers
Woohyeok Jo (Seoul National U.)
Jongil Park (Seoul National U.)
Kyungbae Park (Kangwon National U.)
Abstracts
PDF file
Schedule
August 7 (Fri)
10:30-12:00 Jongil Park
14:00-15:30 Woohyeok Jo
August 8 (Sat)
10:30-12:00 Kyungbae Park
14:00-16:00 Jongil Park & Kyungbae Park
Organizers
JongHae Keum (KIAS)
DongSeon Hwang (IBS-CCG)
Venue
8101, KIAS, Seoul, Korea

Compact Kähler varieties with pseudo-effective tangent sheaf and a dynamical application
2026-08-26 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Guolei Zhong
East China Normal University

Positivity properties of tangent sheaves are known to impose strong restrictions on the global geometry of projective varieties and, more generally, compact Kähler varieties. In this talk, after briefly reviewing the background, we will present several structural results for compact Kähler varieties with pseudo-effective tangent sheaf. As an application to complex dynamics, we will also establish a structure theorem for compact Kähler manifolds admitting a surjective holomorphic self-map with dominant topological degree. The talk is based on joint works with Shin-ichi Matsumura.

Flag variety bundles encoding pseudo-product structures
2026-09-02 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

David Sykes
IBS-CCG

This talk will introduce a natural construction for encoding codimension 1 pseudo-product structures into filtered manifolds amenable to analysis by Tanaka prolongation techniques, and its application to local geometry of CR hypersurfaces. Classically, Tanaka prolongation has only been applicable to maximally nondegenerate pseudo-product structures, while our new techniques require much less. The construction recursively produces levels in a tower of fiber bundles inheriting filtered manifold structures from the underlying geometry. In successful cases, it produces an induced filtered structure with finite-dimensional prolongation, bringing the underlying pseudo-product structure equivalence problems into the scope of classical Tanaka prolongation techniques. As a practical demonstration, we will cover the general construction applied to $(2k+3)$-dimensional $k$-nondegenerate CR hypersurfaces, a complete description of the resulting filtered manifolds’ Tanaka symbols, and their algebraic prolongations. The talk is based on joint work with Boris Doubrov and Igor Zelenko.

Models for elliptic surfaces with a bisection
2026-09-04 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Sönke Rollenske
Marburg University

In the study of (relatively minimal) elliptic surfaces $fcolon S to C$ with a section, the Weierstrass model plays an important role. We discuss two different models for elliptic surfaces with a bisection (or more generally an $f$-nef divisor which has degree two on the fibres): a birational model induced by the involution on the general fibre and a relative determinantal model coming from the relative section ring. The presence of multiple fibres gives rise to new phenomena, which will be illustrated for Enriques surfaces or rational elliptic surfaces. (joint work with Anna Ulivi and Aline Zanardini)

Compact complex parallelisable nilmanifolds with unobstructed deformations
2026-09-08 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Sönke Rollenske
Marburg University

Compact quotients of non-abelian complex nilpotent Lie groups are non-Kähler manifolds with trivial canonical bundle, the most prominent example being the Iwasawa manifold. We give a precise characterisation of the (rare) cases where deformations of such manifolds are unobstructed in terms of so-called verbal ideals in free nilpotent Lie-algebras. On our way, we will have to review some basic ideas of deformation theory. (joint work with M. Paulsen and K. Wehler)

TBA
2026-09-09 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Yewon Luke Cho
Gyeongsang National U

TBA

KSBA moduli compactifications and weighted stable hyperplane arrangements
2026-09-10 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Xian Wu
Yonsei University

We begin with an overview of the framework of KSBA (Kollár—Shepherd-Barron—Alexeev) moduli spaces and stable degenerations, emphasizing some phenomena that distinguish the higher-dimensional cases from the Deligne–Mumford moduli of stable curves. We then survey several existing explicit constructions of KSBA compactifications. As a detailed example, we discuss the construction of KSBA weighted stable hyperplane arrangements via geometric invariant theory (GIT) and matroid tilings due to Valery Alexeev. In particular, here GIT is applied on the construction of the family/stable objects rather than on the construction of the compactified moduli space. Finally, we discuss our ongoing joint work with Hanlong Fang, Patricio Gallardo, and Luca Schaffler on an explicit KSBA wall-crossing morphism to the Losev–Manin space.

Cylinders in Fano threefolds
2026-09-17 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

In-Kyun Kim
HCMC KIAS

A variety $X$ is called cylindrical if it contains a Zariski-open subset isomorphic to $Z times mathbb A^1$ for some affine variety $Z$. If such an open subset is the complement of the support of an effective $mathbb{Q}$-divisor $D$ satisfying $D sim_{mathbb Q} -K_X$, then it is called an anticanonical polar cylinder. The study of cylinders in Fano varieties lies at the intersection of birational geometry and affine geometry. In particular, over an algebraically closed field of characteristic zero, a cylindrical Fano threefold is rational. In recent years, many results have been obtained on which Fano varieties admit cylinders and which do not. In this talk, I will discuss several results on the existence and non-existence of cylinders in Fano threefolds, together with some of the main geometric methods used to prove them.

Conference on Complex Geometry
2026-11-09 - 2026-11-13 | IBS Science Culture Center, Daejeon, Korea, Republic of
Speakers
Rodolf Aguilar Aguilar (CIMAT, Guanajuato)
Cong Ding (Shenzhen U.)
Cecil Gachet (U. Bochum)
Jaehyun Hong (IBS-CCG)
Xiaojun Huang (Rutgers U.)
Lucas Kaufmann (U. Orleans)
Yuta Kusakabe (Kyushu U.)
Minseong Kwon (AMSS, Beijing)
Shin-ichi Matsumura (Tohoku U.)
Suichung Ng (ECNU, Shanghai)
Dan Popovici (U. Toulouse)
Vasily Rogov (MPI, Leipzig)
Min Ru (U. Houston)
Aeryeong Seo (Kyungpook National U.)
Laurent Stolovitch (U. Nice)
Sheng-Li Tan (ECNU, Shanghai)
Wing-Keung To (National U. Singapore)
I-Hsun Tsai (National Taiwan U.)
Julie Wang (Academia Sinica, Taipei)
Kwok Kin Wong (Shenzhen U.)
Abstracts
TBA
Schedule
TBA
Organizers
Philippe Eyssidieux (U. Grenoble)
Jun-Muk Hwang (IBS-CCG)
Sung Yeon Kim (IBS-CCG)
Ngaiming Mok (U. Hong Kong)
Venue
Science Culture Center, IBS, Daejeon, Korea
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