Shuang Su, Volumes of Components of Lelong Upper Level Sets
2025-01-22 16:00 - 17:00 (Asia/Seoul) | B236-1, IBS, Korea, Republic of
Speaker

Shuang Su
University of Cologne

In this talk, I will talk about the joint work with Duc-Viet Vu. We establish an optimal upper bound for the volumes of components of Lelong upper level sets of closed positive (1,1)-currents, in terms of non-pluripolar products of currents.

Combinatorics on flag varieties and related topics 2025
2025-02-10 - 2025-02-14 | Ajou University, Suwon, Korea, Republic of
Speakers
Tatsuyuki Hikita (RIMS)
Byung-Hak Hwang (KIAS)
Takeshi Ikeda (Waseda University)
Minyoung Jeon (University of Georgia)
Donggun Lee (IBS-CCG)
Eunjeong Lee (Chungbuk National University)
Seung Jin Lee (Seoul National University)
Mikiya Masuda (OCAMI)
Seonjeong Park (Jeonju University)
Martha Precup (Washington University in St. Louis)
Mark Skandera (Lehigh University)
John Shareshian (Washington University in St. Louis)
Foster Tom (Massachusetts Institute of Technology)
Organizers
Soojin Cho (Ajou University)
Yunhyung Cho (Sungkyunkwan University)
Jaehyun Hong (IBS-CCG)
JiSun Huh (Ajou University)
Eunjeong Lee (Chungbuk National University)
Seonjeong Park (Jeonju University)
Venue
Ajou University, Suwon, Republic of Korea
Registration
Please submit Google form by January 10th, 2025.
For details, see https://sites.google.com/view/flagvarieties2025/home.

Sung-Yeon Kim, Real orbits in flag manifolds
2025-02-26 15:00 - 16:30 | B236-1, IBS, Korea, Republic of
Speaker

Sung-Yeon Kim
IBS CCG

Let G​ be a complex semisimple Lie group, P​​ be a parabolic subgroup and G0​​ be a real form of G.​​ Then the flag manifold G/P​​ decomposes into finitely many G0-orbits. The complex structure of G/P​​ yields a natural homogeneous CR manifold structure on the real orbits such that all elements in G0 are CR automorphisms. Among them there is exactly one orbit of minimal dimension, which is compact. Shilov boundary of bounded symmetric domains are the well-known examples of such minimal orbits. In this talk, we study real orbits from the point of view of CR geometry. In particular we study the CR structures on the minimal orbits in Grassmannians.

Sung-Yeon Kim, Proper holomorphic maps between bounded symmetric domains
2025-02-27 15:00 - 16:30 | B236-1, IBS, Korea, Republic of
Speaker

Sung-Yeon Kim
IBS CCG

In this talk, we study the rigidity of proper holomorphic maps f: Ω→Ω‘​​ between irreducible bounded symmetric domains Ω​​ and Ω‘​​. First, we will define the moduli maps induced by f​​. This moduli maps are CR maps between real orbits in flag maniflods. If the rank difference is small, i.e., 2 ≤ rank(Ω‘)< 2 rank(Ω)-1​​, then there exists a moduli map which preserves the VMRT structures on the real orbits. Using this property, we will show that f: Ω → Ω‘​​ is a holomorphic totally geodesic isometric embedding with respect to Kobayashi metrics for certain pairs (Ω, Ω‘)​​. This is a joint work with N. Mok and A. Seo.

Ngoc Cuong Nguyen, Equidistribution of Fekete points on projective manifolds
2025-02-27 17:00 - 18:00 | B236-1, IBS, Korea, Republic of
Speaker

Ngoc Cuong Nguyen
KAIST

We survey recent developments on the speed of convergence of Fekete points on projective manifolds where the equidistribution was proved by Berman and Boucksom (2011). In particular, the convergence speed can be obtained for a large class of polynomially cuspidal compact sets introduced by Pawłucki and Pleśniak (1988). These sets are (Cα, Cα’)-regular in the sense of Dinh, Ma and Nguyen (2017).

Ngoc Cuong Nguyen (KAIST)
2025-03-01 - 2026-02-15
Ngoc Cuong Nguyen
Visitor (2025.3.1-2026.2.15) from KAIST
Office: B248

Workshop on Hyperkähler Varieties and Related Topics
2025-03-10 - 2025-03-13 | B109, IBS, Korea, Republic of
Invited Speakers (three one-hour lectures)
Ekaterina Amerik (HSE U.)
Yoonjoo Kim (Columbia U.)
Zhiyuan Li (SCMS, Fudan U.)
Keiji Oguiso (U. Tokyo)
Abstracts
PDF file
Schedule
March 10 (Monday)
14:00-15:00 Registration
15:00-16:00 Amerik, Lecture I
16:00-16:30 Coffee Break
16:30-17:30 Li, Lecture I
18:00-20:00 Speakers dinner
March 11 (Tuesday)
11:00-12:00 Amerik, Lecture II
12:00-14:00 Lunch
14:00-15:00 Li, Lecture II
15:00-15:20 Coffee Break
15:20-16:20 Kim, Lecture I
16:20-16:40 Coffee Break
16:40-17:40 Oguiso, Lecture I
18:00-20:00 Banquet
March 12 (Wednesday)
11:00-12:00 Kim, Lecture II
12:00-14:00 Lunch
14:00-15:00 Oguiso, Lecture II
15:00-15:20 Coffee Break
15:20-16:20 Amerik, Lecture III
16:20-16:40 Coffee Break
16:40-17:40 Li, Lecture III
18:00-20:00 Speakers dinner
March 13 (Thursday)
11:00-12:00 Kim, Lecture III
12:00-14:00 Lunch
14:00-15:00 Oguiso, Lecture III
Organizers
Jun-Muk Hwang (IBS-CCG)
Yongnam Lee (IBS-CCG / KAIST)
Venue
B109, IBS, Daejeon, Korea
Registration
Please submit Google form from February 3 to 23.
More Information
• How to get to IBS-CCG

Lorenzo Barban, General results on C*-actions on projective varieties
2025-03-18 15:00 - 16:30 | B236-1, IBS, Korea, Republic of
Speaker

Lorenzo Barban
IBS CCG

In this lecture series we aim to describe the rich relation between C*-actions on complex normal projetive varieties and the birational maps among the associated geometric quotients. We will begin this first seminar by explaining a motivating example, called the Atiyah flop. We will then discuss general results on normal projective varieties admitting a C*-action, such as Sumihiro’s theorem and Białynicki-Birula theorem. We will then conclude by describing how much a C*-action affects the birational geometry of a C*-variety.

Lorenzo Barban, Geometric Invariant Theory for C*-actions
2025-03-19 15:00 - 16:30 | B236-1, IBS, Korea, Republic of
Speaker

Lorenzo Barban
IBS CCG

In this second talk, which is the technical core of the lecture series, we describe several tools to study C*-actions on projective varieties, such as the bandwidth, the AMvsFM Lemma, and the pruning of a variety. With this, we will be able to describe the -birational geometry of the- geometric quotients of a C* action on a pair (X, L), with X a normal projective variety and L an ample line bundle on X. We will conclude by characterizing C*-varieties with small bandwidth.

Lorenzo Barban, Geometric realization of birational maps among Mori dream spaces
2025-03-20 15:00 - 16:30 | B236-1, IBS, Korea, Republic of
Speaker

Lorenzo Barban
IBS CCG

Given a birational map ϕ among normal projective varieties, a geometric realization of ϕ is a normal projective C*-variety such that the birational map among geometric quotients parametrizing general orbits coincides with ϕ. Geometric realizations can be thought of as a projective algebraic version of the notion of cobordism coming from Morse theory. After recalling basic facts about Mori dream spaces, we show that any birational map among Mori dream spaces admits a geometric realization. In the context of toric varieties, we present a SageMath function to explicitly compute the polytope of the geometric realization. We conclude providing explicit examples of this construction.

Mihai Paun (Universität Bayreuth)
2025-03-26 - 2025-05-02
Mihai Paun
Visitor (2025.3.26-2025.5.2) from Universität Bayreuth
Office: B249

Mihai Paun, Positivity of quotients of holomorphic tensor fields (Lecture I)
2025-03-31 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Mihai Paun
U. Bayreuth

I will present the main results and techniques in the preprint arxiv:2502.02183 (joint with J. Cao). This was motivated by the recent preprint by W. Ou, cf. arXiv:2501.1808 (especially by the algebraicity criteria for foliations on compact Kähler manifolds in this article).
The first lecture is dedicated to the proof of the aforementioned algebraicity criteria. Two main techniques are coming into the picture here. One is the usual substitute for the absence of ample line bundles on compact Kähler manifolds, i.e. the Monge-Ampère equation (combined with the mass concentration method). The second one concerns basic properties of Lelong numbers of closed positive currents.
In the second lecture I will survey a few results concerning the positivity of direct images, and the finally I will explain the proof of the main results (i.e. the complete generalisation to the Kähler case of the results obtained in collaboration with F. Campana).

Mihai Paun, Positivity of quotients of holomorphic tensor fields (Lecture II)
2025-04-01 11:00 - 12:00 | B236-1, IBS, Korea, Republic of

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture I)
2025-04-02 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Thibaut Delcroix
Université de Montpellier

In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a moment map μ and associated moment polytope Δ=μ(X). We fix a weight function v:Δ → (0,+∞), then replace the volume form ωn by v ◦ μ ωn. One can then define new canonical Kähler metrics: weighted solitons and weighted cscK metrics (introduced by Lahdili), which include most classical canonical Kähler metrics.
I will first introduce this weighted setting, then the (analytic) weighted delta invariant, a number that encodes the existence of weighted solitons. I will then present a sufficient condition of existence of weighted cscK metrics, in line with the J-flow approach of Song-Weinkove. Then I will focus on the semisimple principal fibration cosntruction, a construction of varieties from a principal torus bundle and a fiber. The link with weighted Kähler geometry is that, under assumptions on the principal bundle, the Kähler geometry of the total space reduces to the weighted Kähler geometry of the fiber.

Mihai Paun, Hermitian-Einstein metrics for stable coherent sheaves and Bogomolov-Gieseker inequality(Lecture III)
2025-04-02 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Mihai Paun
U. Bayreuth

I will survey the main results obtained in the articles arXiv:2501.18088 and arXiv:2405.10003. There will be no “serious” proofs, I will nevertheless try to highlight the main ingredients in our arguments.

Jinhyung Park, Effective gonality theorem on weight-one syzygies of algebraic curves
2025-04-03 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Jinhyung Park
KAIST

In 1986, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality gon(C) of a smooth projective curve C of genus g can be read off from weight-one syzygies of a sufficiently positive line bundle L, and also proposed possible least degree of L, that is 2g+gon(C)-1. In 2015, Ein-Lazarsfeld proved the conjecture when deg(L) is sufficiently large, but the effective part of the conjecture remained widely open and was reformulated explicitly by Farkas-Kemeny a few years ago. We show an effective vanishing theorem for weight-one syzygies, which implies that the gonality conjecture holds if deg(L) is at least 2g+gon(C) or equal to 2g+gon(C)-1 and C is not a plane curve. As Castryck observed that the gonality conjecture may not hold for a plane curve when deg(L)=2g+gon(C)-1, this result is the best possible and thus gives a complete answer to the gonality conjecture. This is joint work with Wenbo Niu.

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture II)
2025-04-04 14:00 - 15:00 | B236-1, IBS, Korea, Republic of

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture III)
2025-04-07 14:00 - 15:00 | B236-1, IBS, Korea, Republic of

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture IV)
2025-04-09 14:00 - 15:00 | B236-1, IBS, Korea, Republic of

Long Li, Plurisubharmonic functions and Sasaki geometry
2025-04-16 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Long Li
ShanghaiTech University

In this talk, we will discuss the recent progress on the zero mass conjecture for plurisubharmoinc functions, raised by Guedj and Rashkovskii. For a local plurisubharmonic function with an isolated singularity at the origin, the conjecture states that the zero Lelong number (at the singularity) implies the zero residual Monge-Ampere mass at the same point. We confirm this conjecture under the circular symmetry condition, with the aid from Sasaki geometry. Furthermore, we will also apply our technique to more general plurisubharmonic functions in certain cases.

Jie Liu, Symplectic singularities arising from cotangent bundles
2025-04-18 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Jie Liu
AMSS

I’ll report joint works with Baohua Fu (AMSS), in which we investigate symplectic singularities arising from the affinization of the cotangent bundle of a smooth variety.

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 | 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.

Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations I
2025-05-20 10:30 - 12:00 | 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.

Gian Pietro Pirola, Asymptotic directions on the moduli space of curves
2025-05-20 16:00 - 17:00 | 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 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
