会议动机: 几何学在数学中占据着至关重要的地位，通过运用代数、分析、拓扑等多种方法研究几何，实现了将数学的各个领域紧密地联系在一起。模空间作为几何研究的核心之一，扮演着连接相似几何结构的纽带角色。近年来，几何与模空间的研究取得了许多关键性突破，同时也催生了一系列新的研究方向。在这一背景下，我们计划于二零二四年七月在浙江大学举办为期两周的“几何与模空间”学术会议。旨在介绍相关领域的前沿成果，促进来自不同学术背景的学者之间的交流，并致力于培养年轻学者的研究成长。我们期望，此次会议将成为一个有益的合作平台，为数学领域的新发展提供契机。
会场: 浙江大学紫金港圆正·启真酒店四楼阳明厅（校区外酒店东南入口进入，注意不是圆正启真水晶酒店）
联系人: 于飞 (yufei@zju.edu.cn)
7月1-5日报告人: 陈琪乐，陈亦飞，杜荣，方博汉，郭帅，胡勇，胡智， 贾甲，刘克峰，刘治宇，吕鑫，谈胜利，魏传豪，杨晓奎，余讯， 袁瑶，张诗卓，张通，张翼华，张子宇，郑志伟，宗正宇，左康
7月8-12日报告人: 陈柯，范祐维，韩喆，何翔，胡正宇，黄意，冀诸超，蒋云峰，李方，李琼玲，李志远，聂鑫，潘会平，邱宇，阮勇斌，苏伟旭，孙哲，田志宇，王俭，王新，吴云辉，杨迪，张迎春，赵辉，赵永强
部分参会人员网页: 杨金榜，孙悦然，徐万元，孙浩，陆俊，杨文，李晓斌，罗强华，陆斯成，朱胜茂，刘小雷，谭东，钟友良，李灵光，龚成
报告日程:
| 时间 | 7月1日 | 7月2日 | 7月3日 | 7月4日 | 7月5日 |
|---|---|---|---|---|---|
| 9:00-9:50 | 左康 | 陈琪乐 | 杨晓奎 | 谈胜利 | 张子宇 |
| 9:50-10:10 | 茶歇 | ||||
| 10:10-11:00 | 张翼华 | 胡勇 | 张通 | 郑志伟 | 刘治宇 |
| 11:00-11:20 | 茶歇 | ||||
| 11:20-12:10 | 陈亦飞 | 吕鑫 | 杜荣 | 宗正宇 | 张诗卓 |
| 12:10-14:30 | 午餐 | ||||
| 14:30-15:20 | 刘克峰 | 方博汉 | 自由活动 | 袁瑶 | 余讯 |
| 15:20-15:40 | 茶歇 | ||||
| 15:40-16:30 | 郭帅 | 魏传豪 | 贾甲 | 胡智 | |
| 18:00 | 晚餐 |
| 时间 | 7月8日 | 7月9日 | 7月10日 | 7月11日 | 7月12日 |
|---|---|---|---|---|---|
| 9:00-9:50 | 李方 | 阮勇斌 | 苏伟旭 | 李琼玲 | 陈柯 |
| 9:50-10:10 | 茶歇 | ||||
| 10:10-11:00 | 蒋云峰 | 孙哲 | 范祐维 | 冀诸超 | 王新 |
| 11:00-11:20 | 茶歇 | ||||
| 11:20-12:10 | 邱宇 | 黄意 | 韩喆 | 何翔 | 赵辉 |
| 12:10-14:30 | 午餐 | ||||
| 14:30-15:20 | 吴云辉 | 潘会平 | 自由活动 | 聂鑫 | 胡正宇 |
| 15:20-15:40 | 茶歇 | ||||
| 15:40-16:30 | 杨迪 | 李志远 | 王俭 | 赵永强 | |
| 16:30-16:50 | 茶歇 | ||||
| 16:50-17:40 | 田志宇 | 张迎春 | |||
| 18:00 | 晚餐 |
报告信息:
左康 (武汉大学)
题目: Maps into moduli spaces and generic rigidity
摘要: Introducing the notion of generic rigidity for maps into moduli spaces of projective manifolds with good minimal model.
We conjecture that a moduli space, which fails being the generic rigidity, is a Shimura variety of rank >1. We shall discuss some evidences to this conjecture. This is a joint project with Chen-Hu-Sun.
张翼华 (清华大学)
题目: Characterization of non ergodic directions in branched double covers of Veech surfaces
摘要: A closed Riemann surface together with a holomorphic 1-form on it defines a translation surface, which is none other than a section of the canonical line bundle of the Riemann surface. The collection of all such sections forms a bundle of the moduli space of closed Riemann surfaces, sometimes referred to as the Hodge bundle. The existence of an action of SL(2,R) on this bundle is one of the main sources of interplay between geometry and dynamics on moduli spaces. When the SL(2,R)-orbit is closed, its projection to moduli space is called a Teichmuller curve and the any holomorphic 1-form with this property is called a Veech surface. Translation surfaces are themselves interesting geometric structures, e.g. they exhibit a 1-parameter family of directional flows and in the case of Veech surfaces as discovered in 1989, these flows exhibit a certain dichotomy: they are either completely periodic or uniquely ergodic. In this talk, I will describe a different kind of dichotomy discovered in 2011 by Cheung-Hubert-Masur that arises from the investigation of the Hausdorff dimension of the set of nonergodic directions. This result relies on an extension of Masur’s divergence obtained by Cheung-Eskin in 2007, which allowed for the characterization of non ergodic directions in the case of branched double covers of flat tori. Recently, my student Yuming WEI has shown how to extend the dichotomy Hausdorff dimension result to the general case of branched double covers of tori. My goal in this talk is to explain how the characterization of non ergodic directions further extends to certain branhed double covers of Veech surfaces.
陈亦飞 (中国科学院数学所)
题目: Jordan property of automorphism groups of surfaces of positive characteristic
摘要: A classical theorem of C. Jordan asserts the general linear group $GL_n$ over a field of characteristic zero is Jordan.
That is, any finite subgroup of G contains a normal abelian subgroup of index at most J, where J is an integer only depends on the group G.
For the Cremona group of rank n, which is the birational automorphism group of the projective space of dim n, J.-P. Serre proved that the Cremona group of rank 2 has Jordan property. Serre conjectured that the Cremona group of rank n has Jordan property. Prokhorov and Shramov proved the Cremona group of rank 3 has Jordan property, and they pointed out Serre’s conjecture holds if the boundedness of Fano varieties conjecture (BAB conjecture) holds. As the BAB conjecture is proved by the Fields medalist Caucher Birkar, Serre’s conjecture holds. In this talk, we will discuss Jordan property for automorphism groups of surfaces of positive characteristic. This is a joint work with C. Shramov.
刘克峰 (重庆理工大学)
题目: Intersection theory on moduli space of super Riemann surfaces
摘要: The intersection theory on moduli space of super Riemann surfaces was related to Jackiw-Teitelboim (JT) gravity, which is a simple theory of two-dimensional quantum gravity. We will talk about our works on the super version of recursion formulas of higher Weil-Petersson volume, generalizing the formula of Stanford-Witten. We will also talk about polynomiality, asymptotics of intersection numbers and their applications.
郭帅 (北京大学)
题目: A generalization of Witten’s Conjecture through spectral curve
摘要: By reviewing the history of the developments related to the Witten conjecture, we found that all the integrable hierarchies mentioned above are reductions of (multi-component) KP hierarchy. Furthermore, they all have an underlying global spectral curve in the sense of topological recursion. In this talk, we will proposed a generalization of Witten’s conjecture. We then focus on the case when there is only one boundary in the spectral curve, and we explain the idea of the proof for this case. This is base on a joint work with Ce Ji and Qingsheng Zhang.
陈琪乐（美国波士顿学院）
题目: Campana rational connectedness
摘要: The notion of Campana points were introduced by Campana and Abramovich, which interpolate between rational points and integral points. In this talk, we will focus on the geometric side and introduce Campana rational connectedness—a version of rational connectedness for varieties with simple normal crossings boundaries. We futher prove that over function fields, weak approximations by Campana points at good places hold assuming Campana rational connectedness of fibers, generalizing a theorem of Hassett and Tschinkel. We futher verify Campana ratioanl connectedness for many basic examples. Our apporoach relies on the theory of stable log maps and their moduli. This is a joint work with Brian Lehmann and Sho Tanimoto.
胡勇 (上海交通大学)
题目: Noether inequality for irregular threefolds of general type
摘要: Let $X$ be a smooth irregular $3$-fold of general type.
In this talk, we will prove that the optimal Noether inequality $Vol(X) \ge \frac{4}{3}p_g(X)$ holds if $p_g(X) \ge 16$ or if $X$ has a Gorenstein minimal model.
Moreover, when $X$ attains the equality and $p_g(X) \ge 16$, its canonical model will be explicitly described. This is a joint work with Tong Zhang.
吕鑫 (华东师范大学)
题目: The canonical map of a foliated surface of general type
摘要: In this talk, we will report our study on the canonical map of a foliated surface of general type, which generalizes Beauville’s work on the canonical map of an algebraic surface of general type.
Several boundedness results are proved as well as some interesting examples are constructed.
As an application, we establish the Noether type inequalities for foliated surfaces of general type.
方博汉 (北京大学）
题目: Oscillatory integrals in mirror symmetry
摘要: I will describe the oscillatory and period integrals on the B-side of mirror symmetry. They correspond to Gromov-Witten primary and descendant invariants of Gamma-modified twisted Chern classes of the mirror coherent sheaves. The cycles for integration correspond to these mirror sheaves by homological mirror symmetry, and one may obtain higher genus invariants if using correct higher genus B-model integrands. I will explain some examples in the setting of toric mirrors and Gross-Hacking-Keel mirror LG models, and discuss application to Gamma conjectures in the toric setting.
魏传豪 (西湖大学)
题目: On the Hodge theory of Toroidal embeddings and corresponding Vanishings
摘要: Deligne’s logarithmic comparison theorem and the degeneracy of the spectural sequence of logarithmic de Rham complex gives the mixed Hodge structure of a projective smooth variety with a normal crossing boundary divisor. In this talk, we will try to build a similar theory on toroidal embeddings. In particular, we will show the $E_1$-degeneracy of the spectral sequence of the logarithmic de Rham complex of any toroidal triple. This gives a geometric proof of a more general version of Danilov’s conjecture.
杨晓奎 (清华大学)
题目: Geometric positivity and rational connectedness
摘要: In this presentation, we shall talk about several characterizations of rationally connected varieties by using positivity notions in differential geometry and algebraic geometry.
张通 (华东师范大学)
题目: Threefolds on the Noether line
摘要: It is known by J. Chen, M. Chen and C. Jiang that every complex smooth threefold $X$ of general type with $p_g(X) \ge 11$ satisfies the Noether inequality $Vol(X) \ge 4/3 p_g(X) - 10/3$.
If $X$ attains the equality, it is said to be on the Noether line.
In this talk, I will introduce what we know so far about threefolds on the Noether line.
This is a joint work in progress with S. Coughlan, Y.Hu, and R. Pignatelli.
杜荣 (华东师范大学)
题目: A Chern numbers identity on compact Kahler-Einstein manifolds and its applications
摘要: For compact Kahler-Einstein manifolds, we find an expression of Chern numbers in the form of the holomorphic sectional curvatures at a fixed point by means of algebraic invariant theory.
As applications, we obtain a so-called reverse Miyaoka-Yau’s inequality and improve the classical 1/4-pinched theorem and negative 1/4-pinched theorem for compact Kahler-Einstein manifolds to a smaller pinching constant.
Moreover, we confirm Yau’s conjecture on positive holomorphic sectional curvature and Siu-Yang’s conjecture on negative holomorphic sectional curvature if the absolute value of the holomorphic sectional curvature is small enough.
谈胜利 (华东师范大学)
题目: 代数曲面叶层化和庞加莱问题
摘要: 我们将介绍代数曲面叶层化和庞加莱问题的研究历史与最新进展。
郑志伟 (清华大学)
题目: Recent progresses on locally symmetric varieties with modular meaning
摘要: An important topic in complex algebraic geometry is to realize moduli spaces of special objects as locally symmetric varieties via Hodge theory.
Well-known examples include moduli of polarized abelian varieties, Deligne-Mostow theory (moduli of weighted points on projective line), moduli of cubic hypersurfaces of dimension at most 4, moduli of polarized K3 surfaces, etc. I will first survey the existing results and ideas. Then I will introduce a new work with Chenglong Yu about several families of Calabi-Yau manifolds having periods in complex hyperbolic balls.
宗正宇 (清华大学)
题目: Open WDVV equations for toric Calabi-Yau 3-folds
摘要: The Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations is an important system of equations in the study of
genus zero Gromov-Witten invariants. It implies the associativity of the quantum product. The associativity of the quantum product has many important applications including the recursive formula given by Kontsevich and Manin that calculates the Gromov-Witten invariants of the projective plane. The system of open WDVV equations plays an important role in the study of open Gromov-Witten invariants. It can be viewed as an extension of the WDVV equation to the open sector. The natural structure that captures the WDVV equation is that of a Frobenius manifold. Similarly, the system of open WDVV equations determines the structure of an F-manifold, a generalization of a Frobenius manifold. In this talk, we prove two versions of open WDVV equations for toric Calabi-Yau 3-folds. The first version leads to the construction of a semi-simple (formal) Frobenius manifold and the second version leads to the construction of a (formal) F-manifold. This is a joint work with Song Yu.
袁瑶 (首都师范大学）
题目: Sheaves on non-reduced curves in a projective surface
摘要: 1-dimensional sheaves on a surface are torsion sheaves supported at curves in the surface. Hence they are of rank zero. If we consider the moduli space of semistable 1-dimensional sheaves with determinant and Euler characteristic, then in general there are sheaves supported at singular curves. The Hilbert-Chow morphism sends each sheaf to its support. The fibers of over integral curves are isomorphic to their (compactified) Jacobians, while those over non-integral curves are more complicated to understand. We estimate the dimension of the moduli stack of pure sheaves supported at the non-reduced curve with an integral curve. We then get that have all its fibers of the same dimension for a Fano surface or a surface with numerically trivial canonical line bundle, if |L| contains integral curves. The strategy is to firstly deal with the case with smooth and then do induction on the arithmetic genus of which can decrease by a blow-up given singular.
贾甲 (清华大学)
题目: Sheaf stable pairs and birational geometry
摘要: We build bridges between moduli theory of sheaf stable pairs on one hand and birational geometry on the other hand.
We will in particular treat moduli of sheaf stable pairs on smooth projective curves in detail and present some calculations in low degrees.
This is based on a joint work with Caucher Birkar and Artan Sheshmani.
张子宇 (上海科技大学)
题目: Some irreducible components of moduli spaces of stable bundles on hyperkähler manifolds
摘要: Stable sheaves on K3 surfaces have been extensively studied. However, it is a challenging question to construct examples of stable sheaves on hyperkähler manifolds of higher dimensions. In this talk I will present several constructions, which produce irreducible components of the moduli spaces of such sheaves. In particular, one of the constructions yields an irreducible component with non-trivial canonical bundle. Based on joint work with Fabian Reede.
刘治宇 (浙江大学)
题目: Atomic sheaves on hyper-Kähler manifolds via Bridgeland moduli spaces
摘要: Atomic sheaves on hyper-Kähler manifolds have well-behaved Hodge-theoretic properties, and are the natural analogs of simple sheaves on K3 surfaces.
Despiting their nice properties, only a few concrete examples are known on general projective hyper-Kähler manifolds.
In this talk, I will first review the theory of atomic sheaves, then I’ll explain two methods to construct atomic sheaves supported on Lagrangians in the moduli spaces of stable objects in the K3 categories of Gushel-Mukai fourfolds.
If time permits, I’d like to talk about an explicit example of atomic Lagrangians in a hyper-Kähler fourfold and relate it to a conjectural construction of new deformation types of hyper-Kähler manifolds.
This is based on the joint work with Hanfei Guo.
张诗卓（MSRI/晨兴数学中心）
题目: Recent advances on categorical Torelli problems
摘要: Let X be a Fano variety(not necessarily smooth) and denote the non-trivial semi-orthogonal component by \Ku(X), known as the Kuznetsov component. The categorical Torelli problem asks if \Ku(X) determines the isomorphism class of X. I will briefly talk about the history of this topic, including the known results and popular strategies to prove these results(Hodge theoretic, moduli space theoretic and Chow theoretic). Then, I will survey the recent advances for (weighted) hypersurfaces, a cubic threefold with a geometric involution, del Pezzo threefold of Picard rank one, and a class of nodal prime Fano threefolds. Meanwhile, I will talk about some new approaches to solving these problems. If time permits, I will also speak about categorical Torelli problems for a class of index one prime Fano threefold as the double cover of del Pezzo threefolds. This talk is based on a series of works with Xun Lin, Zhiyu Liu, Soheyla Feyzbakhsh, Jorgen Renneomo, Xianyu Hu, Sabastian-Casalaina Martin, and Zheng Zhang.
余讯（天津大学）
题目: Automorphism groups of smooth hypersurfaces
摘要: In this talk, I will discuss some recent results about classifying automorphism groups of smooth hypersurfaces in the projective space. This talk is based on joint works with Keiji Oguiso, Li Wei, Song Yang, and Zigang Zhu.
胡智（南京理工大学）
题目: Parabolic moduli space in nonabelian hodge theory
摘要: In this talk，we discuss parabolic objects in non-abelian Hodge theory and their moduli spaces.
李方（浙江大学）
题目: Combinatorial Methods of Cluster Algebras and Some Related Problems
摘要: Combinatorial methods are important in the theory of cluster algebras, involving graphs, Riemannian surfaces, combinatorial topology, polytopes, and etc. This talk will give an introduction to the combinatorial methods involved in our researches and some results obtained from them related to some important topics in cluster algebras, including the positivity of cluster variables, the positivity of denominator vectors, the polytope basis and the unistructurality of cluster algebras, etc.
蒋云峰 (美国堪萨斯大学)
题目: A SL_r/PGL_r-correspondence for algebraic surfaces
摘要: For a real 4-dimensional manifold (a smooth projective surface in algebraic geometry) X, the S-duality conjecture implies that we should consider the moduli spaces of stable SL_r-Higgs bundles and stable PGL_r-Higgs bundles on X.
The invariants defined by perfect obstruction theories on such moduli spaces are called the Vafa-Witten invariants, which were defined by Tanaka-Thomas in the SL_r side, and by Jiang-Kool in the PGL_r side.
In this talk I will talk about the PGL_r/SL_r-correspondence for the Vafa-Witten invariants for these two sides in both K3 surfaces and general type surfaces.
邱宇 (清华大学)
题目: Moduli spaces of quadratic differentials: Abel-Jacobi map and deformation
摘要: We study the moduli space of quadratic differentials with simple zeros and prescribed polar type.
We prove the fundamental group of which equals the kernel of Abel-Jacobi map.
Then we discuss the partial compactification (with orbifolding) and categorification.
吴云辉 (清华大学)
题目: Prime geodesic theorem and closed geodesics for large genus
摘要: In this work, we study the Prime Geodesic Theorem for random hyperbolic surfaces.
As an application, we show that as the genus g goes to infinity, on a generic hyperbolic surface in the moduli space of Riemann surfaces of genus g, most closed geodesics of length significantly less than $\sqrt{g}$ are simple and non-separating, and most closed geodesics of length significantly greater than $\sqrt{g}$ are non-simple, confirming a conjecture of Lipnowski-Wright. This is a joint work with Yuhao Xue.
杨迪 (中国科学技术大学)
题目: Computations on Masur–Veech volumes of moduli spaces of quadratic differentials
摘要: Based on the Chen–M"oller–Sauvaget formula, we apply the theory of integrable systems to derive three Painle'e-type equations for the generating series of the Masur–Veech (MV) volumes associated with the principal strata of the moduli spaces of quadratic differentials, and propose refinements of the conjectural formulas given by Delecroix–Goujard–Zograf–Zorich on the large genus asymptotics of the MV volumes.
We will also apply the Delecroix–Goujard–Zograf–Zorich formula and Witten’s intersection numbers to the study of the large genus asymptotics of the MV volumes.
The talk is based on arXiv:2005.02275, arXiv:2110.06774.
阮勇斌（浙江大学）
题目: Counting Curves in Calabi-Yau 3-folds
摘要: Counting holomorphic curves in a Calabi-Yau 3-fold is a central problem in physics. It partially motivated the development of Gromov-Witten theory. Over the years, many powerful techniques were developed to solve the problem in non-Calabi-Yau cases. The original case of Calabi-Yau 3-folds remains to be the most difficult cases. Thanks to the contributions of a group of very talented young mathematicians, we are finally bringing the problem to a satisfactory conclusion.
孙哲 (中国科学技术大学)
题目: Exponential volumes of moduli spaces of hyperbolic surfaces
摘要: A decorated surface S is an oriented topological surface with marked points on the boundary considered modulo the isotopy.
The ideal hyperbolic structure on S is the hyperbolic structures on S with geodesic boundary such that the hyperbolic structure near each marked point is a cusp, equipped with a horocycle near each such cusp. We consider the moduli space M_S(K,L) of ideal hyperbolic structures on S, which carries a canonical volume form that generalizes the Weil-Petersson volume form. But the volume of the space M_S(K,L) is infinite when the set of marked points is non-empty, also for its variation without horocycles.
To fix this problem, we introduce the exponential volume form given by the volume form multiplied by the exponent of a canonical function on M_S(K,L).
We show that the exponential volume is finite. And we prove the recursion formulas for the exponential volumes, generalising Mirzakhani’s recursions for the volumes of moduli spaces of hyperbolic surfaces. We expect the exponential volumes are relevant to the open string theory. This is a joint work with Alexander Goncharov.
黄意（清华大学）
题目: The earthquake metric
摘要: We (try to) give a friendly guide for shearing between hyperbolic surfaces in as ``efficient” a manner as possible. On the way, we’ll see Teichmueller spaces, Thurston’s earthquake theorem, and a novel metric on Teichmueller space called the earthquake metric which has surprising connections to both the Thurston metric and the Weil-Petersson metric. This is work in collaboration with K. Ohshika, H. Pan and A. Papadopoulos.
潘会平 (华南理工大学)
题目: Algebraic intersection for hyperbolic surfaces
摘要: How much can two curves of given length intersect each other? In this talk, we will discuss the algebraic intersection form of hyperbolic surfaces. We will show that the algebraic intersection form has a minimum in the moduli space and that the minimum grows in the order $(\log g)^{-2}$ in terms of the genus. We will also describe the asymptotic behavior in the moduli space. This is a joint work with Manman Jiang.
李志远 (复旦大学)
题目: Canonical cycles on moduli space of projective K3 surfaces and beyond
摘要: In this talk, I will survey some results on studying algebraic cycles on moduli space of projective (marked) K3 surface.
This includes the construction of tautological ring, Deligne-Beilinson cohomology of universal K3 surfaces and computation of Chern classes of tagent bundles of the moduli space.
田志宇 (北京大学)
题目: Homological stability and space of curves on some varieties
摘要: Homological stability about moduli space of curves, or mapping class groups, is by now well-understood. I will discuss a set of conjectures as an attempt to understand homological stability of moduli space of curves on a very special class of varieties, such as the projective space, especially about their asymptotic behavior as the curve class becomes more and more positive. This talk will be mostly about motivations, questions, some non-trivial evidence, but very few answers.
苏伟旭 (中山大学)
题目: Thurston volume of the unit balls associated to quadratic differentials
摘要: Let q be a holomorphic quadratic differential on a compact Riemann surface.
We can associate q with a flat metric and a unit ball of the measured lamination space.
We study the Thurston volume of the unit ball and give lower and upper bounds for the volume function on the moduli space.
This is a joint work with Shenxing Zhang.
范祐维 (清华大学)
题目: Dynamical aspects of categories
摘要: We will recall certain analogy between Teichmuller theory and triangulated categories, and discuss categorical results that are motivated from Teichmuller dynamics.
Some open questions will be mentioned if time permitted.
韩喆 (河南大学)
题目: Groupoids from moduli space of quadratic differentials on Riemann surfaces
摘要: By Bridgeland-Smith’s seminal work, the meromorphic quadratic differentials on compact Riemann surface could be realized as stability conditions on some triangulated categories. In this talk, I will introduce a groupoid given by cell structure of the moduli space of meromorphic quadratic differentials. Furthermore, I will explain the connection between the groupoid and topology of the moduli space.
This is a joint work with A. King and Y. Qiu.
李琼玲（南开大学）
题目: Harmonic metrics on Higgs bundles over non-compact surfaces
摘要: For a Higgs bundle over a compact Riemann surface of genus at least 2, the Hitchin-Kobayashi correspondence says the existence of a harmonic metric is equivalent to the polystability of the Higgs bundle. In this talk, we discuss some recent progress on the existence and uniqueness of harmonic metrics on Higgs bundles over general non-compact Riemann surfaces. This is joint work with Takuro Mochizuki.
冀诸超 (西湖大学)
题目: The Dynamical André-Oort conjecture for rational maps
摘要: This is a joint work with Junyi Xie.
We prove the Dynamical André-Oort (DAO) conjecture proposed by Baker and DeMarco for families of rational maps parameterized by an algebraic curve.
In fact, we prove a stronger result, which is a Bogomolov type generalization of DAO for curves.
何翔 (清华大学)
题目: Balancing properties of tropical moduli maps
摘要: Tropical varieties collects the combinatorial data of degenerations of algebraic varieties.
In this talk, we explain how the tropicalization of a family of algebraic curves forms a family of tropical curves, and describe certain balancing conditions of the induced map to moduli space of tropical curves. If time permits, we will also discuss applications to liftability of tropical curves and irreducibility of Severi varieties. This is joint work with Karl Christ and Ilya Tyomkin.
聂鑫 (东南大学)
题目: Circle pattern and discrete conformality
摘要: We give a survey of two closely related objects of study in discrete geometry: circle patterns and discrete conformal equivalence of polyhedral surfaces.
The former deals with patterns of round circles on a surface whose combinatorics/topology is fixed, while the radii of circles may vary; the latter is a discrete analgoue of the usual conformal equivalence of Riemannian metrics. We will focus on the link between both subjects with hyperbolic geometry and Teichmüller spaces, and discuss some recent progress and open problems.
王俭（南开大学）
题目: The positive fundamental group of Sp(2n)
摘要: In this talk, we examine the homotopy classes of positive loops in Sp(2n). We demonstrate that two positive loops are homotopic if and only if they are homotopic through positive loops. This provides a positive answer to a conjecture raised by McDuff. As a consequence, we extend several results of McDuff and Chance to higher dimensional symplectic manifolds without dimensional restrictions. This is a joint work with Qinglong Zhou.
张迎春（浙江大学）
题目: A cluster algebra structure in the quantum cohomology ring of a quiver variety
摘要: In this talk, I will propose a relation between cluster algebras and quantum cohomology rings of quiver varieties. In particular, I will prove this relation for A and D type quivers.
This is a joint work with Weiqiang He.
陈柯（南京大学）
题目: On Shimura subvarieties away from the Torelli locus
摘要: Coleman-Oort conjecture predicts that Shimura subvarieties in the Siegel modular variety A_g should not be contained generically in the Torelli locus when the genus is large enough. We discuss examples supporting the conjecture using geometry of surface fibrations. This is based on joint works with Kang Zuo and Xin Lv.
王新（山东大学）
题目: Virasoro conjecture for Hodge integrals with target varieties and its applications
摘要: Motivated by Eguchi-Hori-Xiong-Katz’s Virasoro conjecture and their genus-0 $\widetilde{L}_n$ constraints for Gromov-Witten invariants, we propose
Virasoro conjecture for general Hodge integrals with target varieties. Then we talk about recent progress about this conjecture and its applications.
赵辉（中科院软件所）
题目: Computational Discrete Global Geometric Structures
摘要: Computational discrete global geometric structures refers to designing algorithm for various global geometric structures, and then applying them to various industrial applications. For example, CADCAE industrial software is currently a bottleneck technology with a huge market. These softwares mainly function on two-dimensional surfaces and three-dimensional entities, and therefore rely on the in-depth application of low-dimensional differential geometry and topology theories. Conversely, extensive industrial applications will also drive the study and research of these related differential geometry and topology theories. We discuss several core technical problems in CADCAE industrial software at present: a) Isogeometric analysis, b) T-Spline splines, c) Finite element analysis, d) Hex hexahedron generation, e) Quad quadrilateral generation, f) Spline surfaces, g) Subdivision; The solutions to these problems require the use of geometric structures such as Riemann surfaces, foliation structures, differential forms, translation surfaces, semi-translation surfaces, moduli spaces, Strata, Teichmüller spaces, holomorphic quadratic differentials, Thurston’s surface mapping classes, square-tiling，saddle connection，ribbon graph, Veech surfaces，etc. Finally, we demonstrate some experimental pictures and videos of applying these low-dimensional differential geometry and topology theories for algorithm design to solve them.
胡正宇（重庆理工大学）
题目: Generalised MMP and boundedness of generalised pairs
摘要: In this talk I will introduce a generalised version of minimal model program (MMP). I will first talk about our motivation to construct such MMP: the boundedness of generalised pairs of general type. A similar result on usual pairs was proved by Hacon-McKernan-Xu, which relies on MMP in families and their approach involves a deep result from complex analysis. Our recent work focuses on ``generalised” MMP in families via a purely algebraic approach. This is a joint work with Caucher Birkar.
赵永强（西湖大学）
题目: On the multiplicity of eigenvalues of discrete tori
摘要: It is well known that the standard flat torus T^2=R^2/Z^2 has arbitrarily large Laplacian-eigenvalue multiplicies. Consider the discrete torus C_N * C_N with the discrete Laplacian operator; we prove, however, that the eigenvalue multiplicities are uniformly bounded for any N, except for the eigenvalue one when N is even. In fact, similar phenomena also hold for higher-dimensional discrete tori. In this talk, we will outline a proof of the uniformly bounded multiplicity result.
交通:
杭州西站: 开车约13公里，地铁约50分
杭州东站: 开车约18公里，地铁约50分
杭州站: 开车约19公里，地铁约54分
杭州南站: 开车约42公里，地铁约1小时20分
萧山国际机场: 开车约45公里，地铁约1小时25分
重要交通枢纽都有地铁，网约车和出租车专门接送口
最近地铁口: 2号线虾龙圩站（距酒店1.1公里）
经费支持: 面上基金 No.11871422 Teichmüller动力学相关问题研究，107100*194212403 中央国库经费，107100+194412404 省国库经费