Center for Complex Geometry

Progress in Complex Geometry
2025-04-21 - 2025-04-24 | B109, IBS, Korea, Republic of
The goal of the workshop is to INTRODUCE some of the most interesting recent developments in complex geometry to (young) people working in areas related to complex geometry. For this purpose, the speakers will try to make the talks understandable to broad audience.
Invited Speakers
2-hours lectures
Bin Guo (Rutgers U.)
Shigeharu Takayama (U. Tokyo)
David Witt Nyström (Chalmers U.)
1-hour talks
Damian Brotbek (U. Lorraine)
Young-Jun Choi (Pusan National U.)
Jie Liu (AMSS, CAS)
Shinichi Matsumura (Tohoku U.)
Dror Varolin (Stony Brook U.)
Juanyong Wang (AMSS, CAS)
Ming Xiao (U.C. San Diego)
Junyi Xie (Peking U.)
Abstracts
PDF file
Schedule
Monday (21st)
Chair: Jun-Muk Hwang
10:00-11:00 Witt Nyström
11:30-12:30 Witt Nyström
Chair: Yongnam Lee
15:00-16:00 Liu
16:30-17:30 Matsumura
Tuesday (22nd)
Chair: Ngoc Cuong Nguyen
10:00-11:00 Guo
11:30-12:30 Guo
Chair: Sungyeon Kim
15:00-16:00 Xie
16:30-17:30 Xiao
18:00-20:00 Banquet
Wednesday (23rd)
Chair: DongSeon Hwang
10:00-11:00 Takayama
11:30-12:30 Takayama
Chair: Thibaut Delcroix
15:00-16:00 Choi
16:30-17:30 Wang
Thursday (24th)
Chair: Mihai Paun
10:00-11:00 Brotbek
11:30-12:30 Varolin
Organizers
Jun-Muk Hwang (IBS CCG)
Mihai Paun (Bayreuth)
Venue
B109, IBS, Daejeon, Korea
Registration
Please submit Google form by April 6.
More Information
• How to get to IBS-CCG

Ilya Kossovskiy, Divergence in CR Geometry
2025-05-07 16:00 - 17:00 (Asia/Seoul) | B236-1, IBS, Korea, Republic of
Speaker

Ilya Kossovskiy
SUSTech

In this lecture, I will outline convergence and divergence phenomena for mappings of CR submanifolds in complex space. Possible applications for mappings of more general geometric structures will be also concerned.

Meng Chen, The Noether inequality for algebraic threefolds
2025-05-08 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Meng Chen
Fudan University

In this talk, I will present a complete proof for the following theorem: the inequality K3 ≥ 4/3 pg-10/3 holds for all 3-folds of general type.

Meng Chen, On the classification of some 3-folds with small positive canonical volumes
2025-05-14 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Meng Chen
Fudan University

In this lecture, I will report some new progress in studying moduli spaces of algebraic 3-folds with very small canonical volume.

JongHae Keum, Fake quadric surfaces
2025-05-19 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

JongHae Keum
KIAS

A smooth projective complex surface S is called a Q-homology quadric if it has the same Betti numbers as the smooth quadric surface. Let S be a Q-homology quadric. Then its cohomology lattice is of rank 2, (even or odd) unimodular. By the classification of surfaces, S is either rational or of general type. In the latter case, S is called a fake Q-homology quadric (fake quadric, in short). There is an unsolved question raised by Hirzebruch: does there exist a surface of general type which is homeomorphic to the smooth quadric surface? I will report recent progress on these surfaces.

Gian Pietro Pirola, Asymptotic directions on the moduli space of curves
2025-05-20 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Gian Pietro Pirola
University of Pavia

We present some computational improvements that allow us to study asymptotic lines in the tangent of the moduli space Mg of the curves of genus g. The asymptotic directions are those tangent directions that are annihilated by the second fundamental form induced by the Torelli map. We give examples of asymptotic lines for any g > 3 and we study their rank. The rank r(v) of a tangent direction at Mg is defined to be the rank of the cup product map associated to the infinitesimal deformation map, that is the infinitesimal variation of Hodge structure in that direction. We show that if v is not zero and r(v)< (cliff(C) + 1) where cliff(C) is the Clifford index of C, then v is not asymptotic and we study the case when r(v)= cliff(C). Finally all asymptotic directions of rank 1 are determined and a description of the rank 2 case is given. It is a joint work with Elisabetta Colombo and Paola Frediani.

Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations I
2025-05-20 16:00 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Benjamin McMillan
IBS CCG

Foliations have a theory of characteristic classes that is much like that of vector bundles, but with notable differences. Some of the characteristic classes of a foliation come from its induced normal bundle, but there are additional secondary classes that depend on more detailed information about the foliation. Just as with vector bundles, one can obtain the characteristic classes using either a universal space or the Chern-Weil construction (in case the foliation is regular).
In these talks I will explain the general theory, and how the Chern-Weil construction can often be made to work even for singular foliations.

Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations II
2025-05-21 16:00 - 17:30 | B236-1, IBS, Korea, Republic of

Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations III
2025-05-22 11:00 - 12:00 | B236-1, IBS, Korea, Republic of

Sanghyeon Lee, Vafa-Witten invariants on elliptic surfaces and moduli space of quasisections
2025-05-22 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Sanghyeon Lee
Ajou University

For a threefold X = C x S, D. Nesterov developed a theory of quasimaps from C to the moduli space of sheaves over S. He compared the moduli space of quasimaps and the moduli space of sheaves over the threefold X and also compared their obstruction theories.
When X is a smooth fibration over C, I will explain how to generalize Nesterov’s theory by using a notion of quasisections, instead of quasimap, and the correspondence between moduli space of sheaves over X and the moduli space of quasisections to the relative moduli space of sheaves. As an application, I will explain how to compute Vafa-Witten invariants of an elliptic surface, which is a smooth fibration over C.
Moreover, for the case when the elliptic surface has nodal fibers, we will discuss how we can generalize the theory of quasisections. This is based on an ongoing project with Yaoxiong Wen.

Gian Pietro Pirola, Sections of the Jacobian bundles of plane curves and applications
2025-05-27 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Gian Pietro Pirola
University of Pavia

We study normal functions (sections of the Jacobian bundle) defined on the moduli space of pointed plane curves. Using the infinitesimal Griffiths invariant (refined by M. Green and C. Voisin) we show that a normal function with nontrivial but sufficiently “small” support cannot be “locally constant”. As an application, we give a variational proof of the following result of Zu:
Theorem: If C is a very general plane curve of degree d and C’ is any plane curve of degree d’, then the cardinality i(C, C’) of the intersection between C and C’ is > d-3.
We also show that if d > 3 and i(C, C’) = d-2 then d’ = 1 and C’ is a bitangent or a flex line. For d = 4 this is a result of Chen, Rield and Yeong. This is a joint work with Lorenzo Fassina.

Han-Bom Moon (Fordham University)
2025-06-08 - 2025-06-14
Han-Bom Moon
Visitor (2025.6.8-2025.6.14) from Fordham University

Han-Bom Moon, Ulrich bundles on intersections of quadrics
2025-06-09 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Han-Bom Moon
Fordham University

An Ulrich bundle is a vector bundle with very strong cohomology vanishing conditions. Eisenbud and Schreyer conjectured that every smooth projective variety possesses an Ulrich bundle. Despite many results on low dimensional varieties and special varieties, the general existence is unknown. In this talk, I will describe recent work in progress with Kyoung-Seog Lee and Jiwan Jeong on the construction of Ulrich bundles on an intersection of quadrics.

Patrick Brosnan (University of Maryland)
2025-06-23 - 2025-07-05
Patrick Brosnan
Visitor (2025.6.23-2025.7.5) from University of Maryland

Sung Gi Park, Hodge symmetries of singular varieties
2025-06-24 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Sung Gi Park
Princeton U. / IAS

The Hodge diamond of a smooth projective complex variety exhibits fundamental symmetries, arising from Poincaré duality and the purity of Hodge structures. In the case of a singular projective variety, the complexity of the singularities is closely related to the symmetries of the analogous Hodge-Du Bois diamond. For example, the failure of the first nontrivial Poincaré duality is reflected in the defect of factoriality. Based on joint work with Mihnea Popa, I will discuss how local and global conditions on singularities influence the topology of algebraic varieties.

Alex Abreu (Universidade Federal Fluminense)
2025-06-25 - 2025-07-05
Alex Abreu
Visitor (2025.6.25-2025.7.5) from Universidade Federal Fluminense

Yoosik Kim, Disk Counting via GIT Quotients
2025-06-26 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Yoosik Kim
Pusan National University

According to the Kempf–Ness theorem, the GIT quotient is equivalent to the symplectic reduction. Using this correspondence, we explain how to relate the counting of holomorphic disks between a symplectic manifold equipped with a Hamiltonian group action and its symplectic reduction. As an application, we derive the disk potential function for weight varieties obtained as quotients by the maximal torus of partial flag varieties. We also demonstrate how the disk counting depends on the choice of stability conditions.

Alex Abreu, On the Torelli Theorem for graphs and stable curves
2025-06-27 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Alex Abreu
Universidade Federal Fluminense

The classical Torelli theorem states that a smooth curve can be recovered from its polarized Jacobian. In this talk, we will discuss the extensions of this theorem to stable curves and their dual graphs, as well as its dependence on the concept of compactified Jacobians. First, we will recall Caporaso and Viviani’s theorem, which characterizes when two stable curves have the same Caporaso’s compactified Jacobian. Then we will discuss Torelli’s theorem via fine compactified Jacobians. This is based on an ongoing joint work with Marco Pacini and Nicola Pagani.

Workshop on Hessenberg varieties, Lusztig varieties, and Affine Grassmannians
2025-06-30 - 2025-07-04 | B109, IBS, Korea, Republic of
This workshop brings together experts in Hessenberg varieties, Lusztig varieties, and the affine Grassmannian. It focuses on the rich interactions among these geometric objects and their connections to representation theory and combinatorics. Recent breakthroughs and new developments will be presented and discussed. The workshop aims to foster collaboration and inspire future research.
Invited Speakers
Lectures
Alex Abreu (Universidade Federal Fluminense)
Pramod Achar (Louisiana State University) *
Research Talks
Hiraku Abe (Okayama University of Science)
Donggun Lee (IBS CCG)
* (online)
Abstracts
PDF file
Lecture Note
Pramod Achar (Louisiana State University): Notability link
Schedule
Monday (June 30)
10:00-11:00 Alex Abreu
11:30-12:30 Pramod Achar
12:30-14:00 Lunch
14:00-16:00 Open Problems
16:00-18:00 Tea Break/Free Discussion
18:00- Speakers Dinner
Tuesday (July 1)
10:00-11:00 Alex Abreu
11:30-12:30 Pramod Achar
12:30-14:00 Lunch
14:00-16:00 Free Discussion
16:00-18:00 Tea Break/Free Discussion
18:00- Banquet
Wednesday (July 2)
10:00-11:00 Alex Abreu
11:30-12:30 Pramod Achar
12:30-14:00 Lunch
14:00-16:00 Free Discussion
16:00-18:00 Tea Break/Free Discussion
18:00- Speakers Dinner
Thursday (July 3)
10:00-11:00 Donggun Lee
11:30-12:30 Hiraku Abe
12:30-14:00 Lunch
Friday (July 4)
10:00-12:00 Open Problems
12:30-14:00 Lunch
Organizers
Patrick Brosnan (University of Maryland)
Jaehyun Hong (IBS CCG)
Donggun Lee (IBS CCG)
Venue
B109, IBS, Daejeon, Korea
Registration
Please submit Google form by June 26 (Thu).
There will be open problem sessions. To suggest open problems/questions, complete google form by June 23 (Mon).
More Information
• How to get to IBS-CCG

Yoonjoo Kim, Two results on Lagrangian fibrations
2025-07-02 15:00 - 16:00 | B236-1, IBS, Korea, Republic of
Speaker

Yoonjoo Kim
Columbia U.

I would like to report two ongoing results on Lagrangian fibrations of smooth symplectic varieties. The first is the construction of a delta-regular smooth group scheme that acts on a given Lagrangian fibration. It is a generalization of the result of Arinkin-Fedorov, who proved the result under the assumption that every fiber is integral. The second is the computation of the degree of the discriminant divisor of a Lagrangian fibration, assuming the total space is a (projective) hyper-Kähler manifold. This resolves a question raised by Sawon, who first discovered the formula and proved it under the assumption that every general singular fiber is integral. The first result is joint work with Mark de Cataldo and Christian Schnell.

Hyukmoon Choi, Equivariant compactification structures on smooth projective horospherical varieties of Picard number 1
2025-08-07 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Hyukmoon Choi
IBS CCG and KAIST

A projective variety V is an equivariant compactification of an algebraic group G if there exists an algebraic G-action on V with a Zariski open orbit O, which is equivariantly biregular to G. Such a G-action is called an equivariant compactification (EC) structure on V. For a smooth nonhomogeneous projective horospherical variety X of Picard number 1, and for a suitable nilpotent subgroup N of the automorphism group of X, we show that X admits an EC structure of N and that any two EC structures of N on X are isomorphic.

Makoto Enokizono, Normal stable degenerations of Noether-Horikawa surfaces
2025-08-27 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Makoto Enokizono
University of Tokyo

Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the equality of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) Classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Criterion for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Description of the KSBA moduli spaces for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.

Doyoung Choi, Singularities and syzygies of secant varieties of smooth projective varieties
2025-08-28 15:00 - 16:00 | B236-1, IBS, Korea, Republic of
Speaker

Doyoung Choi
KAIST / IBS

We study the higher secant varieties of a smooth projective variety embedded in projective space. We prove that when the variety is a surface and the embedding line bundle is sufficiently positive, these varieties are normal with Du Bois singularities and the syzygies of their defining ideals are linear to the expected order. We show that the cohomology of the structure sheaf of the surface completely determines whether the singularities of its secant varieties are Cohen-Macaulay or rational. We also prove analogous results when the dimension of the original variety is higher and the secant order is low, and by contrast we prove a result that strongly implies these statements do not generalize to higher dimensional varieties when the secant order is high. Finally, we deduce a complementary result characterizing the ideal of secant varieties of a surface in terms of the symbolic powers of the ideal of the surface itself, and we include a theorem concerning the weight one syzygies of an embedded surface — analogous to the gonality conjecture for curves — which we discovered as a natural application of our techniques.

Haesong Seo, Algebraic hyperbolicity of adjoint linear systems on spherical varieties
2025-08-28 16:30 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Haesong Seo
KAIST / IBS

A projective manifold is called hyperbolic if it does not admit an entire map from the complex plane. Demailly proved that hyperbolic manifolds are algebraically hyperbolic, meaning that there are degree bounds for curves in terms of their genera. It is a highly challenging problem to determine whether a given variety is algebraically hyperbolic or not. In this talk, we prove that a very general hypersurface in an adjoint linear system on a spherical variety is algebraically hyperbolic outside the boundary. This is based on a joint work with Dr. Minseong Kwon.

Qifeng Li, Minimal rational curves on equivariant compactifications of symmetric spaces
2025-09-11 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Qifeng Li
Shandong University

Let X be a smooth equivariant compactification of a symmetric space. In this talk, we will discuss when a minimal rational curve on X is the orbit closure of a 1-parameter group. In case the symmetric space is of group type, the answer is positive and moreover the VMRT is the closure of an adjoint orbit. This generalizes a result of Brion and Fu’s on wonderful compactifications to arbitrary equivariant compactifications. This is a joint work with Jun-Muk Hwang.

Yong Hu, Moduli spaces of threefolds on the Noether line
2025-09-11 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Yong Hu
Shanghai Jiao Tong University

In this talk, we will introduce the 3-dimensional Noether inequality and completely classify the canonical threefolds on the Noether line with $p_g ge 5$ by studying their moduli spaces. For every such moduli space, we establish an explicit stratification, estimate the number of its irreducible components and prove the dimension formula. A new and unexpected phenomenon is that the number of irreducible components grows linearly with the geometric genus, while the moduli space of canonical surfaces on the Noether line with any prescribed geometric genus has at most two irreducible components of the same dimension. This is a joint work with S.Coughlan, R.Pignatelli and T.Zhang.

Minseong Kwon, Automorphism groups of toroidal horospherical varieties
2025-10-02 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Minseong Kwon
Gyeongsang National University

In the 1970s, Demazure studied the automorphism groups of two types of almost homogeneous varieties: rational homogeneous spaces and toric varieties. Especially, for a smooth complete toric variety, Demazure obtained a structure theorem for the connected automorphism group in terms of the so-called Demazure roots. In this talk, I will discuss the connected automorphism group of a smooth complete toroidal horospherical variety, which can be viewed as a fiber bundle over a rational homogeneous space with toric fibers. Namely, I will introduce a notion of roots as a generalization of the Demazure roots, and then utilize it to describe the structure of the connected automorphism group. As a consequence, a reductivity criterion for the connected automorphism group will be presented. This talk is based on a joint work with Lorenzo Barban and DongSeon Hwang.

Moduli of Surfaces and Beyond
2025-11-03 - 2025-11-07 | IBS Science Culture Center, Daejeon, Korea, Republic of
Speakers
Lecture Series (3hr)
Radu Laza (Stony Brook University)
Matthias Schütt (Leibniz Universität Hannover)
Jenia Tevelev (University of Massachusetts Amherst)
Research Talks (1hr)
Kenneth Ascher (University of California, Irvine)
Dori Bejleri (University of Maryland, College Park)
Harold Blum (Georgia Institute of Technology)
Nathan Chen (Harvard University)
Changho Han (Korea University)
Donggun Lee (IBS-CCG)
Samouil Molcho (Sapienza Università di Roma)
Giancarlo Urzua (Pontificia Universidad Católica de Chile)
Abstracts
PDF file
Schedule

Mon
Tue
Wed
Thu
Fri

10:00~11:00
Registration
Schütt 2
Schütt 3
Urzua
Han

11:00~11:30
Coffee break
Coffee break
Coffee break
Coffee break
Coffee break

11:30~12:30
Schütt 1
Laza 2
Laza 3
Ascher
Chen

12:30~14:30
Lunch
Lunch
Lunch
Lunch
Lunch

14:30~15:30
Laza 1
Tevelev 2
Tevelev 3
Bejleri
Lee

15:30~16:00
Coffee break
Coffee break
Coffee break
Coffee break

16:00~17:00
Tevelev 1
Molcho

Blum

17:30~20:00
Dinner for Speakers
Banquet
Dinner for Speakers
Dinner for Speakers

Organizers
DongSeon Hwang (IBS-CCG)
Donggun Lee (IBS-CCG)
Yongnam Lee (IBS-CCG)
Venue
IBS Science Culture Center, Daejeon, Korea
Registration
Please submit Google form by October 15.
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

Cauchy-Riemann Symmetry and Real Hypersurfaces in Hermitian Symmetric Spaces
2025-12-11 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Jong Taek Cho
Chonnam National University

We survey recent developments of pseudo-Hermitian geometry or CR geometry of hypersurface type, with a particular focus on their symmetries and realizations as real hypersurfaces in Hermitian symmetric spaces.

Perspectives in algebraic geometry
2025-12-15 - 2025-12-19 | B109, IBS, Korea, Republic of
The talks will begin on December 16, following a day of free discussion on December 15.
Confirmed Speakers
Lorenzo Barban (IBS-CCG)
Junho Choe (KIAS)
Karl Christ (University of Turin)
Fei Hu (Nanjing University)
Sukmoon Huh (Sungkyunkwan University)
Jaehyun Kim (Ewha Womans University)
Jeong-Seop Kim (KIAS)
Shin-Young Kim (Kangwon National University)
Haidong Liu (Sun Yat-sen University)
Wenfei Liu (Xiamen University)
Gebhard Martin (University of Bonn)
Sheng Meng (ECNU)
Sung Gi Park (Princeton University)
Luca Rizzi (IBS-CGP)
Haesong Seo (KAIST/IBS-CCG)
Lei Song (Sun Yat-sen University)
Claudia Stadlmayr (University of Neuchâtel)
Sho Tanimoto (Nagoya University)
Wern Yeong (UCLA)
Abstracts
PDF file
Schedule

Mon
Tue
Wed
Thu
Fri

09:30~10:00
Free discussion & seminar (TBA)
Registration

10:00~10:50
Karl christ
Lei Song
Sukmoon Huh
Wern Yeong

11:10~12:00
Sung Gi Park
Junho Choe
Wenfei Liu
Haesong Seo

12:00~14:00
Lunch
Lunch
Lunch
Lunch

14:00~14:50
Lorenzo Barban
Claudia Stadlmayr
Jeong-Seop Kim
Luca Rizzi

15:10~16:00
Shin-young Kim
Fei Hu
Jaehyun Kim
Gebhard Martin

16:20~17:10
Haidong Liu
Sheng Meng
Sho Tanimoto

17:40~20:00
Dinner for Speakers
Banquet
Dinner for Speakers
Dinner for Speakers

(There will be a coffee/tea break between talks each day.)
Organizers
DongSeon Hwang (IBS-CCG)
Jun-Muk Hwang (IBS-CCG)
Yongnam Lee (IBS-CCG)
Venue
B109, IBS
Registration
Please submit Google form by November 30.
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
