Algebraic geometry and complex geometry are two central pillars of modern mathematics, deeply interconnected and rich in applications. Algebraic geometry focuses on algebraic structures such as varieties, moduli spaces, and related objects, while complex geometry investigates the intricate properties of complex manifolds and analytic spaces. These fields not only influence each other profoundly but also share powerful research tools, including Hodge theory and the minimal model program (MMP).

To promote academic exchange and foster collaboration among researchers in these vibrant areas, we are pleased to announce the “Workshop on Algebraic Geometry and Complex Geometry”, to be held at Wuhan University from August 31 to September 9, 2025.

Time: August 31, 2025 to September 9, 2025

Venue: Lei Jun Science and Technology Building, Wuhan University

Organizing committee: 

Huai-Liang Chang (Wuhan University, China)

Sheng Rao (Wuhan University, China)

Jiangwei Xue (Wuhan University, China)

Kang Zuo (Wuhan University, China)

Schedule：

Short course instructors:

Academic conference Speakers：

Short talks:

Title and Abstract(Continuously updating):

Short courses

Title:

Theory of singular Hermitian metrics on vector bundles and its applications

Shin-ichi Matsumura

Tohoku University, Japan

Abstract:

In this series of lectures, I will present the theory of singular Hermitian metrics on vector bundles from the basics,and then discuss an attempt to generalize several structure theorems proved by Demailly–Peternell–Schneider (1994) formulated for compact Kahler manifolds with nef tangent bundle.Specifically, I will focus on the following topics:

(1) Singular Hermitian metrics on vector bundles;

(2) Analytic positivity of direct images and the L2-extension theorem with optimal estimates;

(3) Structure theorems for compact Kahler manifolds with pseudo-effective tangent bundle.

Title:

Kobayashi-Hitchin correspondences for periodic monopoles and related topics

Takuro Mochizuki

Kyoto University, Japan

Abstract:

It is one of the significant themes in complex differential geometry to find a correspondence between differential geometric objects and algebraic geometric objects. Several years ago, we established equivalences between periodic monopoles and difference modules, which are analogous to the equivalences between harmonic bundles, Higgs bundles, and flat bundles. With this goal in mind, in this lecture, we shall explain topics including (1) instantons, monopoles, and harmonic bundles, (2) equivalences of harmonic bundles and $\lambda$-flat bundles, (3) monopoles and mini-holomorphic structure, (4) stable parabolic difference modules, and (5) Kobayashi-Hitchin correspondences for periodic monopoles.

Title:

Singularity formation in Kahler geometry

Song Sun

Zhejiang University, China

Abstract:

I will explain the understanding of singularity formation of canonical metrics on Kahler manifolds, with an emphasis on the interaction between geometric analysis and algebraic geometry. In particular, we will explain the bubbling phenomenon and discuss a uniform picture connecting Kahler-Ricci shrinkers and Fano fibration. The latter brings together various topics studied separately in previous works, including Kahler-Einstein metrics, Sasaki-Einstein metrics and Kahler-Ricci flows.

Title:

Introduction to Hodge structure and Shimura varieties

Liang Xiao

Peking University, China

Abstract:

I will first introduce the concept of Hodge structures and its variation. This is closely related to the concept of Shimura varieties. If time permits, I will discuss briefly discuss Deligne's theorem on absolute Hodge classes.

Talks

Title:

On the Kodaira Dimension

Osamu Fujino

Kyoto University, Japan

Abstract:

There is a well-known conjecture concerning the subadditivity of the Kodaira dimension, often referred to as the Iitaka conjecture. On the other hand, Popa conjectured that the Kodaira dimension is superadditive for smooth morphisms. In this talk, I will explain how Popa’s conjecture on the logarithmic Kodaira dimension can be derived from a generalized abundance conjecture. This is a joint work with Taro Fujisawa.

Title:

NC Grassmann variety as an NC moduli space

Yujiro Kawamata

The University of Tokyo, Japan

Abstract:

The aim is to construct a non-commutative Grassmann variety NCG(m,n) which satisfies the following conditions:

(1) It is an NC scheme which is constructed by gluing NC algebras.  

(2) The set of closed points is the same as the usual Grassmann variety G(m,n).  

(3) At each closed point, the completion of the NC algebra is the parameter algebra of the semi-universal NC deformation of the corresponding linear subspace in a fixed projective space.

(4) There is a universal family of linear subspaces on it. We prove the existence for NCG(2,4).

Title:

Infinite dimensional algebra and instanton moduli spaces

Wei-Ping Li

The Hong Kong University of Science and Technology, China

Abstract:

Given a projective smooth surface X and its blowup surface Y, Yoshioka calculated the blowup formula relating Betti numbers of the moduli space of rank two sheaves on X with those on Y. Nakajima asked the question of a representation theoretic interpretation of the blowup formula. In the joint work with QIngyuan Jiang and Yu Zhao, we studied the representation of an extended Clifford algebra on the cohomology of moduli space of stable sheaves on Y and gave an answer to Nakajima’s question.

Title:

Derived isogenous of abelian varieties

Zhiyuan Li

Fudan University, China

Abstract:

In this talk, I will talk about the Fourier-Mukai transformations between twisted varieties. In recent years, people found such transformation is very useful in many aspect, such as Hodge conjecture and Bloch-Beilinson conjecture. Our goal is to give a derived Torelli theorem for twisted abelian varieties and classify the derived isogenous abelian varieties by using the traditional isogenous.

Title:

Automorphic cohomology, Penrose transformation, and geometry of non-classical flag domains.

Kefeng Liu

Chongqing University of Technology, China

Abstract:

I will present my recent joint works with Yang Shen on the geometry and representation theory aspects of non-classical flag domains.

We prove several conjectures of Griffiths about the the structures of automorphic cohomology on compact quotients of non-classical flag domains.

We construct new complex structures on non-classical flag domains D = G_R /V with G_R of Hermitian type and their compact quotients. As applications, we give new examples of compact smooth manifolds on which there are two complex structures with very different geometric properties.

Building on these works, we construct Penrose transformations of the cohomology groups of homogeneous line bundles on flag domains D = G_R /T and identify conditions under which the Penrose transformation of the automorphic cohomology groups on compact quotients of flag domains is an isomorphism. As applications we prove that the higher automorphic cohomology groups of certain homogeneous line bundles are isomorphic to the groups of automorphic forms on the Hermitian symmetric domain.

Title:

Canonical Kähler-Einstein metrics applied to a rigidity problem for irreducible lattices of rank ≥ 2 of the Hermitian type

Ngaiming Mok

The University of Hong Kong, China

Abstract:

Title:

F-trivial vector bundles on curves

Ho Hai Phung

Vietnam Academy of Sciences and Technology, Vietnam

Abstract:

Let X be a proper scheme over a perfect field k of characteristic p>0. F-trivial vector bundles are those vector bundles that become trivial when pulled back by a power of the Frobenius. This concept was introduced by Mehta and Subramanian to study the Nori fundamental group. In this work we report some progress on the study of F-trivial vector bundles on a projective curve.

Title:

Globally F-regularity of moduli spaces of parabolic bundles

Xiaotao Sun

Tianjin University, China

Abstract:

I will report a preprint joint with Mingshuo Zhou, in which we prove that moduli space of parabolic bundles with a fixed determinant on a generic curve is globally F-regular.

Title:

Positively curved Weil-Petersson type metrics on Viehweg-Zuo type sheaves and its singular Griffiths semi-positive extension.

Shigeharu Takayama

The University of Tokyo, Japan

Abstract:

We consider various families of polarized Kaehler-Einstein manifolds. Building on a series of works of W.-K. To and S.-K. Yeung, we show the Viehweg-Zuo type sheaf; a canonically attached sub-sheaf of some symmetric power of the log-cotangent bundle on the base space, admits a natural Weil-Petersson type metric with Griffiths semi-positive curvature. If time permit, we also discuss the (dual) Nakano positivity and the minimum extension property. This is a joint work with W.-K. To and S.-K. Yeung.

Title:

Modular invariants of a fibered algebraic surface and applications

Sheng-Li Tan

East China Normal University, China

Abstract:

The moduli spaces of curves provide us some modular invariants of a fibered algebraic surface, which are generalized to foliated algebraic surfaces. We will talk about the recent progress in the study of these invariants, including Noether's inequalities, partial solutions of Poincare Problem. and the surjectivity of Keller maps.

Title:

Deformations of Dirac operators

Weiping Zhang

Nankai University, China

Abstract:

Dirac operators, as well as their deformations, play important roles in many problems of geometry and topology. We will discuss some aspects of it.

Title:

TBA

Xiangyu Zhou

Academy of Mathematics and Systems Science,CAS, China

Abstract:

TBA

Short Talks

Title:

Fiberwise bimeromorphism and specialization of bimeromorphic types for locally Moishezon families

Jian Chen

Central China Normal University, China

Abstract:

Inspired by the recent works of M. Kontsevich--Y. Tschinkel and J. Nicaise--J. C. Ottem on specialization of birational types for smooth families (in the scheme category) and J. Koll{\'a}r's work on fiberwise bimeromorphism, we focus on characterizing the fiberwise bimeromorphism and utilizing the characterization to investigate the specialization of bimeromorphic types for certain non-smooth families in the complex analytic setting.  We mainly establish some criteria for a bimeromorphic map between two families over the same base to be fiberwise bimeromorphic; and we then utilize these criteria to establish the specialization of bimeromorphic types for families with certain singularities.

This is based on joint works with Professors Sheng Rao and I-Hsun Tsai.

Title:

On the distribution of non-rigid families

Tianzhi Hu

Wuhan University, China

Abstract:

Shafarevich conjecture claims the rigidity property for any non-isotrivial family of projective curves of genus g≥2 over a punctured projective curve base. However, such rigidity property fails for any family of projective varieties. Thus we define non-rigid loci in moduli spaces and make a conjecture on the distribution of non-rigid loci: if there is Zariski dense subset of non-rigid loci in a moduli space, then this moduli space is either a fibration with product fiber, or birational to a Shimura variety of rank≥2. Our conjecture is very strong as we can use it to prove a version of geometric Bombieri-Lang conjecture for a 'general' moduli space. Under some Hodge theoretic assumption, we use the theory of Hodge loci to study our conjecture and we can prove our conjecture for moduli spaces of Calabi-Yau manifolds with Q-simple generic Mumford-Tate group. This is a joint work with Ke Chen, Ruiran Sun and Kang Zuo.

Participants:

Sponsors:

Tianyuan Mathematical Center in Central China

School of Mathematics and Statistics, Wuhan University

Contact:

Bo Li             algebra@whu.edu.cn

Sheng Rao     likeanyone@whu.edu.cn