On the virtual cohomological dimensions of automorphism groups of K3 surfaces
2026-02-27 16:30 - 17:30 (Asia/Seoul) | 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
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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.

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.

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)
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
More Information
• How to get to IBS-CCG
