Torsion points on holomorphic sections of elliptic surfaces
2026-01-21 15:00 - 16:00 (Asia/Seoul) | 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)
More Information
• How to get to IBS-CCG
• From Hotel to IBS

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
More Information
• How to get to IBS-CCG

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.

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.)
Yuta Kusakabe (Kyushu U.)
Minseong Kwon (AMSS, Beijing)
Suichung Ng (ECNU, Shanghai)
Dan Popovici (U. Toulouse)
Vasily Rogov (MPI, Leipzig)
Min Ru (U. Houston)
William Sarem (U. Grenoble)
Aeryeong Seo (Kyungpook National U.)
Laurent Stolovitch (U. Nice)
Shigeharu Takayama (U. Tokyo)
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
More Information
• How to get to IBS-CCG
