Center for Complex Geometry

Pacific Rim Complex and Symplectic Geometry Conference
2024-07-29 - 2024-08-02 | IBS Science Culture Center, Daejeon, Korea, Republic of
Invited Speakers
Dongwook Choa (KIAS, Seoul)
Young-Jun Choi (Pusan National Univ.)
Siarhei Finski (École Polytechnique)
Hervé Gaussier (Univ. Grenoble-Alpes)
Masafumi Hattori (Kyoto Univ.)
Siqi He (AMSS, Beijing)
Ludmil Katzarkov (Univ. Miami)
Yusuke Kawamoto (ETH, Zurich)
Takayuki Koike (Osaka Metropolitan Univ.)
Yu-Shen Lin (Boston Univ.)
George Marinescu (Univ. Köln)
Yuichi Nohara (Meiji Univ.)
Semon Rezchikov (Princeton Univ.)
Harish Seshadri (Indian Inst. Science)
Rasul Shafikov (Univ. Western Ontario)
Li-Sheng Tseng (U.C. Irvine)
Seungook Yu (Postech)
Jihun Yum (Gyeongsang National Univ.)
Ruobing Zhang (Princeton Univ.)
Andrew Zimmer (Univ. Wisconsin)
Abstracts
PDF file
Schedule
July 29 (Monday)
(Morning session chaired by Jun-Muk Hwang)
10:00-11:00 Marinescu
11:20-12:20 Choi
12:30-14:00 Lunch
(Afternoon session chaired by Dano Kim)
14:00-15:00 Nohara
15:15-16:15 Gaussier
16:30-17:30 Yum
July 30 (Tuesday)
(Morning session chaired by Kaoru Ono)
10:00-11:00 Seshadri
11:20-12:20 Kawamoto
12:30-14:00 Lunch
(Afternoon session chaired by Yong-Geun Oh)
14:00-15:00 Rezchikov
15:15-16:15 Yu
16:30-17:30 Choa
18:00-20:00 Banquet
July 31 (Wednesday)
(Morning session chaired by Kengo Hirachi)
10:00-11:00 Koike
11:20-12:20 Zhang
12:30-14:00 Lunch
Free Afternoon
August 1 (Thursday)
(Morning session chaired by Jae-cheon Joo)
10:00-11:00 Zimmer
11:20-12:20 Lin
12:30-14:00 Lunch
(Afternoon session chaired by Kyoung-Seog Lee)
14:00-15:00 Katzarkov
15:15-16:15 Finski
16:30-17:30 Tseng
August 2 (Friday)
(Morning session chaired by Sungyeon Kim)
9:30-10:30 He
10:40-11:40 Hattori
11:50-12:50 Shafikov
12:50-14:00 Lunch
Scientific Committee
Xiuxiong Chen (Stony Brook Univ.)
Kengo Hirachi (Univ. Tokyo)
Jun-Muk Hwang (IBS-CCG)
Yong-Geun Oh (IBS-CGP & POSTECH)
Kaoru Ono (RIMS, Kyoto)
Yongbin Ruan (Zhejiang Univ.)
Organizing Committee
Jun-Muk Hwang (IBS-CCG)
Sungyeon Kim (IBS-CCG)
Yong-Geun Oh (IBS-CGP & POSTECH)
Venue
IBS Science Culture Center, Daejeon, Korea
Registration
Please submit Google form.
More Information
• How to get to IBS-CCG

Jiewon Park, Hessian Estimates, Monotonicity Formulae, and Applications
2024-06-26 16:00 - 17:00 (Asia/Seoul) | B236-1, IBS, Korea, Republic of
Speaker

Jiewon Park
KAIST

Various monotonicity formulae have profound applications in many different problems in geometric analysis. Quite often these formulae can be derived from pointwise Hessian estimates, also known as Li-Yau-Hamilton estimates or matrix Harnack inequalities. In this talk we will focus on this connection building upon Hessian estimates for the Green function, leading to novel monotonicity formulae on manifolds with certain curvature lower bounds and Einstein manifolds. Some of the results have counterparts for Kähler manifolds.

Euisung Park, On Rank 3 Quadratic Equations of Projective Varieties
2024-06-25 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Euisung Park
Korea University

Many projective varieties are ideal-theoretically cut out by quadratic polynomials of rank less than or equal to 4. Classical constructions in projective geometry like rational normal scrolls and Segre-Veronese varieties are examples. Regarding this phenomenon, I would like to talk about the following two results in this talk. First, there are many projective varieties cut out ideal-theoretically by quadratic polynomials of rank 3. Second, there is a nice structure of the locus of rank 3 quadratic equations of a projective variety.

Kisun Lee, Numerical Certification and Certified Homotopy Tracking
2024-06-24 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Kisun Lee
Clemson University

A certified algorithm produces a solution and a certificate of correctness to a problem. Numerical certification studies certified algorithms for results obtained from numerical methods in algebraic geometry. In this talk, we discuss why numerical certification is needed in numerical algebraic geometry and introduce the Krawczyk homotopy as one of its methods. The Krawczyk homotopy exploits interval arithmetic to track the homotopy solution path without path jumping so that the correctness of its output is guaranteed. This is joint work with Timothy Duff.

Kisun Lee, Introduction to Numerical Algebraic Geometry
2024-06-24 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Kisun Lee
Clemson University

Numerical algebraic geometry employs numerical techniques for problems in algebraic geometry. This talk begins with a question reminding the meaning of solving a (polynomial) equation. It overviews the homotopy continuation as a method for finding solutions to a system of polynomial equations. After problems from algorithmic and application points of view in numerical nonlinear algebra are introduced, we discuss how the results from numerical techniques can be certified. No pre-knowledge from graduate-level algebraic geometry is assumed.

Myeongjae Lee, Connected Components of the Strata of Residueless Meromorphic Differentials
2024-06-18 11:00 - 12:00 | on-line
Zoom ID: 880 6763 5837
PW: [REDACTED]

Speaker

Myeongjae Lee
Stony Brook University

Strata of differentials are interesting objects studied in various fields such as Teichmuller dynamics, topology and algebraic geometry. Generalized strata are subsets of the strata of meromorphic differentials, where certain sets of residues summing up to zero. We present the classification of the connected components of the strata of residueless meromorphic differentials, using a degeneration technique to the boundary of a nice compactification of strata.

Cheol Hyun Cho, Floer Theory for the Variation Operator of an Isolated Singularity
2024-06-13 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Cheol Hyun Cho
Seoul National University

The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define a new Floer cohomology, called monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the Seifert form. We discuss examples of plane curve singularities and explain the relation between exceptional collections of non-compact curves and distinguished collections of vanishing cycles.

Eric Sommers, Some Slodowy Slices Associated to Special Nilpotent Orbits
2024-06-11 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Eric Sommers
University of Massachusetts

Among the nilpotent orbits in a simple Lie algebra are the special nilpotent orbits, which play an important role in representation theory. Some of the geometry of the closure of a nilpotent orbit can be understood by taking a transverse slice to a smaller orbit in the closure. This talk concerns a classification of two types of such transverse slices: (1) those between adjacent special nilpotent orbits; and (2) those between a special nilpotent orbit and a certain non-special nilpotent orbit in its closure. The slices in part (1) exhibit a duality, which extends an observation of Kraft and Procesi for type A. The slices in part (2) are related to a conjecture of Lusztig on special pieces. This talk is based on two preprints with Baohua Fu, Daniel Juteau, and Paul Levy.

Minyoung Jeon, Prym-Brill-Noether Loci and Prym-Petri Theorem
2024-06-11 11:00 - 12:00 | on-line
Zoom ID: 880 6763 5837
PW: [REDACTED]

Speaker

Minyoung Jeon
University of Georgia

Prym varieties are abelian varieties constructed from etale double covers of algebraic curves. In 1985, Welters equipped Prym varieties with Brill-Noether loci. In this talk, we will describe the Prym-Brill-Noether loci with special vanishing at up to two marked points and will then give K-classes of the pointed and two-pointed Prym-Brill-Noether locus. As applications of the K-class formulas of the Prym-Brill-Noether loci, we will also provide formulas for Euler characteristics of the pointed Prym-Brill-Noether loci and coupled Prym-Petri theorem.

Sung Rak Choi, Adjoint Asymptotic Multiplier Ideal Sheaves
2024-05-23 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Sung Rak Choi
Yonsei University

In this talk, we define and study a triple called a potential triple which consists of a pair (X, Δ) and a polarizing pseudoeffective divisor D.
To such a triple, we define a so-called potential multiplier ideal sheaf which gives a simultaneous generalization of the multiplier ideal sheaf and asymptotic multiplier ideal sheaf. We give a description of the closed subset defined by potential multiplier ideal sheaf in terms of the minimal model program. We also characterize the case where potential multiplier ideal sheaf is trivial. Lastly, we also prove a Nadel type vanishing theorem of cohomology for potential multiplier ideal sheaf. We further present applications of the theory of potential triples. This is a joint work with S.Jang and D.Kim.

Shigeru Mukai, Moduli of Abelian Surfaces, Polyhedral Groups and Fano 3-folds of Degree 22 (Part 2)
2024-05-22 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Shigeru Mukai
RIMS, Kyoto University

I will discuss the moduli space of abelian surfaces with bi-level structure of type (1, d) for d = 2, 3, 4, 5.
Part 1: Their Satake compactification is the projective 3-space P3 for d = 2, 3, 4.
Part 2: It is a small contraction of the blow-up of P3 at 60 points for d = 5. I give two proofs. One is analytic and uses good automorphic forms constructed by Gritsenko-Nilulin. The other is algebraic and uses U22, one of the Umemura 3-folds, and Reye congruences.

Shigeru Mukai, Moduli of Abelian Surfaces, Polyhedral Groups and Fano 3-folds of Degree 22 (Part 1)
2024-05-21 16:00 - 17:00 | B236-1, IBS, Korea, Republic of

Jungkai Chen, Threefold Divisorial Contraction to Curves
2024-05-17 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Jungkai Chen
National Taiwan University

The minimal model program works pretty well in dimension three. However, the explicit classification of divisorial contractions to points was completed quite recently thanks to the work of Kawamata, Hayakawa, Kawakita and more. In this talk, we are going to describe threefold divisorial contractions to curves. We will demonstrate some more possible higher dimensional extensions. This is joint work in progress with Jheng-Jie Chen and Hsin-Ku Chen.

Workshop on Algebraic Geometry in Busan
2024-05-14 - 2024-05-16 | La Valse Hotel, Busan, Korea, Republic of
Speakers
Lorenzo Barban (IBS-CCG)
Jungkai Chen (National Taiwan University)
Toshiyuki Katsura (University of Tokyo)
Shigeyuki Kondo (Nagoya University)
Ching-Jui Lai (National Cheung Kung University)
Donggun Lee (IBS-CCG)
Hsueh-Yung Lin (National Taiwan University)
Shigeru Mukai (Kyoto University)
Keiji Oguiso (University of Tokyo)
Abstracts
PDF file
Schedule
May 14 (Tuesday)
14:00~14:20 Registration
14:20~15:20 Oguiso
15:40~16:40 Lai
17:00~18:00 Lin
18:30~20:30 Dinner
May 15 (Wednesday)
09:30~10:30 Katsura
11:00~12:00 Kondo
12:00~13:30 Lunch
13:30~17:30 Discussion
18:00~20:00 Banquet
May 16 (Thursday)
09:30~10:30 Chen
11:00~12:00 Barban
12:00~13:30 Lunch
13:30~14:30 Lee
15:00~16:00 Mukai
Organizers
JongHae Keum (KIAS)
Yongnam Lee (IBS-CCG/KAIST)
Venue
La Valse Hotel, Busan
* Due to available hotel rooms and budgets, participation is by invitation only. If you are interested to participate in this workshop, please contact one of the organizers by April 15.

Ching-Jui Lai, Anticanonical Volume of Singular Fano Threefolds
2024-05-13 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Ching-Jui Lai
National Cheung Kung University

The set of canonical Fano threefolds form a bounded family by results of Kawamata, Mori-Miyaoka-Kollar-Tagaki, and in a much more general setting by Birkar. In particular, the anticaonical volume –KX3 is bounded. An optimal lower bound is 1/330 by the work of Chen-Chen. In this talk, we discuss the problem of identifying an optimal upper bound of –KX3.

Hsueh-Yung Lin, Motivic Invariants of Birational Automorphisms of Threefolds
2024-05-13 14:30 - 15:30 | B236-1, IBS, Korea, Republic of
Speaker

Hsueh-Yung Lin
National Taiwan University

The motivic invariant c(f) of a birational automorphism f : X – → X measures the difference between the birational types of the exceptional divisors of f and those of the inverse f-1. In general c(f) is nonzero: this is the case when f is some Cremona transformation, which leads to new explanation as to why Cremona groups are not simple. In the other direction, which will be the main focus of the talk, we show that the invariant c(f) always vanishes when X is a complex projective threefold. (joint work in progress with E. Shinder.)

Shigeyuki Kondo, A Review on Enriques Surfaces: Moduli, Automorphism Groups and Positive Characteristics, II
2024-05-08 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Shigeyuki Kondo
Nagoya University

The Enriques surface was discovered, in 1894 by Federigo Enriques, as a counter-example of a rationality problem.
First I would like to recall the moduli space and the automorphism groups of Enriques surfaces over the complex numbers.
In the later half, I shall mention a recent progress in positive characteristic, especially in characteristic two.

Shigeyuki Kondo, A Review on Enriques Surfaces: Moduli, Automorphism Groups and Positive Characteristics, I
2024-05-07 16:00 - 17:00 | B236-1, IBS, Korea, Republic of

Benjamin Bakker, A Proof of Matsushita's Conjecture
2024-04-30 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Benjamin Bakker
Univ. Illinois Chicago

Matsushita conjectured that for any Lagrangian fibration f:X→B of a compact hyperkahler manifold X, the fibers deform either maximally or trivially in moduli. In this talk I’ll explain how to prove this conjecture via Hodge theory. I will also discuss some other features of the topology of Lagrangian fibrations and a result about the density of torsion points in sections. Time permitting, I will discuss some more recent work with C. Schnell from this perspective reproving a result of J.-M. Hwang that B is projective space if it is smooth.

Benjamin Bakker, Hodge Theory and Lagrangian Fibrations
2024-04-29 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Benjamin Bakker
Univ. Illinois Chicago

Compact hyperkahler manifolds X are higher-dimensional generalizations of K3 surfaces; their geometry is tightly constrained by the existence of a holomorphic symplectic form. For example, a result of Matsushita says the only nontrivial fibration structures f:X→B they admit are fibrations by Lagrangian tori. In this talk, I will give an overview of how Hodge theory connects the geometry of B to the variation of these tori in moduli, and how Hodge-theoretic techniques can be used to understand B both locally and globally.

Chuyu Zhou, Wall Crossing for K-stability
2024-04-26 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Chuyu Zhou
Yonsei University

We will introduce a novel characteristic of K-stability, i.e. wall crossing phenomenon, and present a comparison between K-stability and GIT-stability. Time permitting, we will survey some open problems.

Chuyu Zhou, Moduli for Fano Varieties with K-stability
2024-04-25 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Chuyu Zhou
Yonsei University

We will present the construction of moduli space of Fano varieties with K-stability, including defining the moduli functor, showing various good properties of the functor, and introducing Alper-Halpern Leistner-Heinloth criterion for the existence of good moduli space.

Chuyu Zhou, K-stability of Fano Varieties - Various Viewpoints
2024-04-24 11:00 - 12:00 | B236-1, IBS, Korea, Republic of
Speaker

Chuyu Zhou
Yonsei University

We will present various criterion for K-stability for Fano varieties, including viewpoints from test configurations, valuations, and filtrations.

In-Kyun Kim, Wall-crossing of K-moduli Spaces of Weighted Projective Spaces
2024-04-23 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

In-Kyun Kim
KIAS

In algebraic geometry, constructing moduli spaces that parametrize families of algebraic varieties with certain properties is an important problem.
In the case of Fano varieties, the construction of moduli spaces is a challenging problem.
K-stability provides a criterion for selecting nice representatives within the moduli space, which helps create more meaningful and well-behaved moduli spaces.
In this talk, we will study some properties of K-moduli spaces. This is a joint work with Yuchen Liu and Chengxi Wang.

Workshop on Geometry of Homogeneous Varieties
2024-04-15 - 2024-04-18 | B109, IBS, Korea, Republic of
Speakers
Michel Brion (U. Grenoble)
Jarek Buczynski (IMPAN, Warsaw)
Thibaut Delcroix (U. Montpellier)
Minseong Kwon (KAIST/IBS-CCG)
Qifeng Li (Shandong U.)
Yoshinori Namikawa (RIMS, Kyoto)
Kyeong-Dong Park (Gyeongsang National U.)
Boris Pasquier (U. Poitiers)
Léa Villeneuve (U. Poitiers)
Abstracts
PDF file
Schedule
April 15 (Monday)
10:00-11:00 Brion
11:20-12:20 Brion
12:30-13:20 Lunch
15:00-16:00 Kwon
16:20-17:40 Li
April 16 (Tuesday)
10:00-11:00 Pasquier
11:20-12:20 Pasquier
12:30-13:20 Lunch
15:00-16:00 Park
16:20-17:40 Villeneuve
April 17 (Wednesday)
10:00-11:00 Namikawa
11:20-12:20 Namikawa
12:30-13:20 Lunch
Free Afternoon
April 18 (Thursday)
10:00-11:00 Delcroix
11:20-12:20 Delcroix
12:30-13:20 Lunch
15:00-16:00 Buczynski
16:20-17:20 Buczynski
Organizers
Jaehyun Hong (IBS-CCG)
Jun-Muk Hwang (IBS-CCG)
Main Hotel
Lotte City Hotel Daejeon (4-30 Doryong-dong, Yuseong-gu, Daejeon)
Venue
B109, IBS, Daejeon, Korea
Registration
Please submit Google form by March 31.
More Information
• How to get to IBS-CCG

Michel Brion, Introduction to Complete Symmetric Varieties
2024-04-11 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Michel Brion
U. Grenoble

This is an introductory lecture on compactifications of symmetric spaces in algebraic geometry.

Michel Brion, Introduction to Symmetric Spaces
2024-04-09 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Michel Brion
U. Grenoble

This is an introductory lecture on symmetric spaces in algebraic geometry.

Yong Hu, Noether Inequality for Irregular Threefolds of General Type
2024-03-26 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Yong Hu
Shanghai Jiao Tong University

Let X be a smooth irregular 3-fold of general type. In this talk, we will prove that the optimal Noether inequality vol(X) ≥ (4/3) pg(X) holds if pg(X) ≥ 16 or if X has a Gorenstein minimal model. Moreover, when X attains the equality and pg(X) ≥ 16, its canonical model will be explicitly described. This is a joint work with Tong Zhang.

Dennis The, On 4D Split-conformal Structures with G2-symmetric Twistor Distribution
2024-03-21 16:00 - 17:00 | B266, IBS, Korea, Republic of
Speaker

Dennis The
The Artic University of Norway, Tromso

In their 2013 article, An & Nurowski considered two surfaces rolling on each other without twisting or slipping, and defined a twistor distribution (on the space of all real totally null self-dual 2-planes) for the associated 4D split-signature conformal structure. If this split-conformal structure is not anti-self dual, then the twistor distribution is a (2,3,5)-distribution, and An-Nurowski identified interesting rolling examples where it achieves maximal, i.e. G2, symmetry. Relaxing the rolling assumption, a similar construction can be made for any 4D split-conformal structure, and my talk will discuss a broader classification of examples where such exceptional symmetry for the twistor distribution is achieved. (Joint work with Pawel Nurowski & Katja Sagerschnig.)

Boris Doubrov, Bifiltered Parabolic Geometries
2024-03-19 16:00 - 17:00 | B266, IBS, Korea, Republic of
Speaker

Boris Doubrov
Belarusian State University, Minsk

We introduce the notion of a bifiltered manifold and generalizing the constructions of the symbol and Tanaka prolongation from nilpotent differential geometry. Next, we consider bifiltered manifolds modeled by bigradings of simple Lie algebras and show how this generalizes known constructions in the parabolic geometries such as existence of a unique normal Cartan connection. Finally, we show how the language of bifiltered manifolds can be used for uniform treatment of correspondence spaces in parabolic geometries, where the covering space is not necessarily regular in the classical sense.
