Chuyu Zhou, Moduli for Fano Varieties with K-stability
2024-04-25 11:00 - 12:00 (Asia/Seoul) | 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, 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.

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.

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.

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
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, II
2024-05-08 11:00 - 12:00 | B236-1, IBS, Korea, Republic of

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.)

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.

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.

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.

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
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 2)
2024-05-22 16:00 - 17:00 | B236-1, IBS, Korea, Republic of

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.

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.

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.

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.

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.

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.

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.

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.

Jiewon Park, Hessian Estimates, Monotonicity Formulae, and Applications
2024-06-26 16:00 - 17:00 | 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.

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

Sheng Meng, On Surjective Endomorphisms of Projective Varieties
2024-08-06 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Sheng Meng
East China Normal University

Let X be a normal projective variety over C. Let f be a surjective endomorphism of X. In this talk, I will try to explain our current program on the classification and the building blocks of (f, X), involving two main tools: equivariant minimal model program and dynamical Iitaka fibration. Two applications on the Kawaguchi-Silverman conjecture and the Zariski dense orbit conjecture will be given. This is based on several joint works with Junyi Xie, De-Qi Zhang and Guolei Zhong.

Chuyu Zhou, Lecture 1: Constructible Properties of Various Domains for a Family of Couples
2024-08-06 16:00 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Chuyu Zhou
Yonsei University

In this lecture, I will recall some basic knowledge on K-stability and some background on wall crossing in proportional setting. Then we plan to conduct a comparison between proportional case and non-proportional case. Under the comparison, we will define several domains associated to a family of couples and present their constructible properties.

Chuyu Zhou, Lecture 2: Non-linear Wall Crossing Theory
2024-08-07 16:00 - 17:30 | B236-1, IBS, Korea, Republic of
Speaker

Chuyu Zhou
Yonsei University

In this lecture, we will talk about two properties of K-semistable domains in non-proportional setting. One is the finiteness criterion, which states that the number of domains is finite for a family of couples. The other is about the shape of each domain, which states that they are semi-algebraic sets. These two properties together lead to a satisfactory wall crossing theory for K-stability in non-proportional case. Time permits, I will present a comparison between GIT-stability and K-stability in non-proportional setting.

Xiaojun Huang, Bounding a Levi-flat Hypersurface in a Stein Manifold
2024-08-22 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Xiaojun Huang
Rutgers Univ

Let M be a smooth real codimension two compact submanifold in a Stein manifold. We will prove the following theorem: Suppose that M has two elliptic complex tangents and suppose CR points are non-minimal. Assume further that M is contained in a bounded strongly pseudoconvex domain. Then M bounds a unique smooth up to M Levi flat hypersurface M̂ that is foliated by Stein subspace diffeomorphic to the ball. Moreover, M̂ is the hull of holomorphy of M. This subject has a long history of investigation from E. Bishop and Harvey-Lawson. I will discuss both the history and techniques used in the proof of the above mentioned theorem.

Changho Han (한창호, Korea University)
2024-10-13 - 2024-10-14
Changho Han (한창호)
Visitor (2024.10.13-2024.10.14) from Korea University
Office: –

Changho Han, Trigonal Curves and Associated K3 Surfaces
2024-10-14 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

Changho Han
Korea university

K3 surfaces, as a generalization of elliptic curves, have a rich amount of geometric properties. Recalling that elliptic curves are double covers of rational curves branched over 4 distinct points, there are K3 surfaces that are cyclic triple covers of rational surfaces; Artebani and Sarti classified such generic K3 surfaces depending on lattice invariants. Such K3 surfaces admit Kulikov and KSBA degenerations, each leading to toroidal and KSBA compactifications of the moduli spaces of such K3 surfaces. As joint works in progress with Valery Alexeev, Anand Deopurkar, and Philip Engel, I will explain how to use trigonal curves (triple covers of rational curves) to obtain aforementioned degenerations, leading to more explicit understandings of boundaries of those compactifications: such as classifications of generic members and the dimensions.

Justin Lacini, On Log del Pezzo Surfaces in Positive Characteristic
2024-10-15 14:00 - 15:00 | B236-1, IBS, Korea, Republic of
Speaker

Justin Lacini
Princeton university

A log del Pezzo surface is a normal surface with only Kawamata log terminal singularities and anti-ample canonical class. Over the complex numbers, Keel and McKernan have classified all but a bounded family of log del Pezzo surfaces of Picard number one. In this talk we will extend their classification to positive characteristic. In particular, we will prove that for p>3 every log del Pezzo surface of Picard number one admits a log resolution that lifts to characteristic zero over a smooth base. As a consequence, we will see that Kawamata-Viehweg vanishing holds in this setting. Finally, we will conclude with some counterexamples in characteristic two, three and five.

David Sykes, CR Hypersurfaces, Studying 2-nondegenerate Structures via Absolute Parallelisms
2024-10-22 16:00 - 17:00 | B236-1, IBS, Korea, Republic of
Speaker

David Sykes
IBS CCG

The basic problem of finding (local) biholomorphisms mapping one real hypersurface in a complex space onto another is only well understood for a limited class of hypersurfaces, and has a fundamental relationship to their induced CR geometries. Following a light historical survey of major results in the area, this talk will present a solution to the local equivalence problem for 2-nondegenerate CR hypersurfaces, developed in joint work with Igor Zelenko, given by canonically encoding the geometries into absolute parallelisms.
