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短课程:Multiplier ideals, vanishing theorems and applications 2018年12月11日至13日

摘要:We would describe various vanishing theorems involving multiplier ideals and give various applications to linear systems, birational geometry and commutative algebra.

Leavitt path algebras via singularity categories 2020年7月8日 10:00-11:00
*主持人:周国栋 副教授
*时间:2020年7月8日 10:00-11:00
*地点:Zoom 房间号:685 9743 2504 会议密码:164921

Cohen-Macaulay differential graded modules and negative Calabi-Yau configurations 2020年7月6日 14:00-15:00
*主持人:周国栋 副教授
*时间:2020年7月6日 14:00-15:00
*地点:Zoom 房间号:685 9743 2504 会议密码:164921

晋海波,2016年硕士毕业于华东师范大学,即将博士毕业日本名古屋大学,导师国际数学家大会45分钟报告人日本名古屋大学Osamu Iyama教授。

In this talk, we introduce a nice class of dg algebras A ca...
Tilting modules for classical Lie superalgebras 2020年7月2日10:30-11:30
主持人:罗栗 副教授
报告平台:Zoom房间号:873 477 8140 密码:500494

报告人简介: 陈志玮博士,毕业于中国台湾中研院,师从程舜仁教授,从事李超代数表示论研究。现任职于台湾省中央大学。

报告内容简介:A finite-dimensional Lie superalgebra g=g_0+g_1 is called classical if the restriction of the adjoint representation of g to the...
Jantzen Coefficients and radical filtrations for generalized Verma modules 2020年4月29日16:30-17:30
报告人简介: 肖维博士,毕业于香港科技大学。现任职于深圳大学,主要从事李群、李代数的表示论研究。

报告内容简介:We give a sum formula for the radical filtration of generalized Verma modules in any (possibly singular) integral blocks of parabolic BGG category which can be viewed as a generalization of Jantzen sum formula for Verma modules in the usual BGG category O. Combined with Jant...
Gelfand-Kirillov dimensions and associated varieties of highest weight modules 2020年4月29日15:30-16:30
报告人简介: 白占强副教授,博士毕业于香港科技大学。曾在中科院数学与系统科学研究院、武汉大学等科研院校从事博士后研究与教学工作。现任职于苏州大学,主要研究方向为李群、李代数的表示论。

报告内容简介:In this talk, we will introduce the Gelfand-Kirillov dimension and associated variety of highest weight moudles of simple Lie algebras. By using a conjecture of Tanisaki, we will show that...
Minimum positive entropy of complex Enriques surface automorphisms Friday, 12.Apr.2019, 13:30--14:30
Abstract: We determine the minimum positive entropy of complex Enriques surface automorphisms. This together with McMullen's work completes the determination of the minimum positive entropy of complex surface automorphisms in each class of Enriques-Kodaira classification of complex surfaces. As in McMullen's work, we finally reduce the problem to computer algebra. In this talk, after recalling kno...
On the rigidity problem of families of surfaces of minimal model Thursday, 04.Apr.2019, 15:00--16:00
Abstract: we discuss a criterion for rigid families of projective surfaces of minimal model. We propose a conjecture on the decomposition of fibers of non-rigid families.
Perverse sheaves, Lagrangian fibrations, and hyper-Kaehler geometry Friday, 29.Mar.2019, 13:00--14:00
Abstract: The P=W conjecture of de Cataldo, Hausel, and Migliorini relates the topology of Hitchin fibrations to the Hodge theory of character varieties via Simpson’s nonabelian Hodge theory. In recent joint work with Junliang Shen, we proved a compact analog of this conjecture, which relates the topology of Lagrangian fibrations to the Hodge theory of compact hyper-Kaehler manifolds. I will pres...
A note on extremal trigonal fibrations on rational surfaces Wendesday, 27.Mar.2019, 10:30--11:30
Abstract: The Picard number of a rational surface equipped with a relatively minimal trigonal fibration is bounded in terms of the genus $g$ of a general fibre. When the Picard number attains the maximum for $g\geq3$, we describe such a fibred surface whose Mordell-Weil group is trivial. This is a joint work with Cheng Gong (Soochow Univ.) and Jun Lu (East China Normal Univ.).
AR-sequence of Graded Kronecker modules 2019年3月25日下午14:00-15:00
摘要 We talk about the regular indecomposable modules for the covering of the
Kronecker quiver and their Auslander-Reiten sequences.


报告人简介: 刘杰2016年硕士毕业于华东师范大学, 导师舒斌教授,现在德国Kiel大学攻读博士学位,导师 Rolf Farnsteiner 教授,现阶段主要研究 Auslander-Reiten 理论
Inner Projection and Castelnuovo-Mumford regularity for structure sheaves Friday, 22.Mar.2019, 13:00--14:00
Abstract: Noma developed the inner projection method and gave a classification of projective varieties in a sense. As an important consequence, he established a sharp linear bound for Castelnuovo-Mumford regularity of structure sheaves on smooth projective varieties of arbitrary dimension. I will show how blending Noma’s classification with multiplier ideal theory leads to the same bound for norm...
τ-tilting finiteness of two-point algebras 2019年3月20日(星期三)下午14:30至15:30
摘要: τ-tilting theory was introduced by Adachi, Iyama and Reiten, which completes the classical tilting theory from the viewpoint of mutation. They constructed a class of Λ-modules named (support) τ-tilting modules, where Λ is a finite dimensional basic algebra over an algebraically closed field. We call Λ a τ-tilting finite algebra if there are finitely many isomorphism classes of basic τ...
Distribution and foliation on moduli spaces of minimal varieties Wendesday, 20.Mar.2019, 13:00--14:00
Abstract: I shall report some progress in a joint project with Steven Lu and Ruiran Sun in the study of a class of distributions on moduli spaces of minimal varieties. The ultimate goal is to show Borel hyperbolicity of those type moduli spaces.
Decomposition, E_1 degeneration and Vanishing Theorem 3月18日下午14:00至15:00
摘要: Deligne-Illusie in 80s opened the Hodge theory in positive characteristic, by providing an algebraic and elementary proof of the E_1 degeneration theorem and Kodaira's vanishing theorem over a characteristic zero field. The key result in their work is the so-called decomposition theorem for de Rham complexes. In this talk, I shall report our recent work on the decomposition theorem for inter...
BCOV invariant and birational equivalence Friday, 15.Mar.2019, 14:00--15:00
Abstract: The BCOV invariant is an invariant for Calabi-Yau manifolds. In this talk, we extend the BCOV invariant to Calabi-Yau pairs, i.e., a Kahler manifold equipped with a pluricanonical divisor. In certain case, this BCOV invariant is equivalent to an equivariant BCOV invariant introduced by Yoshikawa. Moreover, this BCOV invariant is well-behaved under birational equivalence. We expect that t...
On numerical nonvanishing for generalized log canonical pairs Friday, 15.Mar.2019, 13:00--14:00
Abstract: The notion of generalized polarized pairs was introduced by Birkar and Zhang to deal with the effectivity of Iitaka fibration. Its prototype already appeared in the treatment of the canonical bundle formula for elliptic fibrations. The notion has since found more and more applications in solving problems for usual pairs. In the other direction, efforts have been made by several authors t...
Hall algebras and i-quantum groups 2019-3-14 下午 13:30-14:30
王伟强教授任职于美国弗吉尼亚大学数学系,是国际上极具影响力的表示论研究专家。他的重要工作发表在《Inv. Math.》, 《Duke Math. J.》等诸多数学顶级杂志上,总被引次数过千。他还著有Graduate Studies in Mathematics系列第144卷 《Dualities and representations of Lie superalgebras》。同时王伟强教授还担任国际一流数学期刊 《Int. Math. Res. Not.》 的编委。

Birational geometry in the LC cateogory Friday, 08.Mar.2019, 14:00--15:00
Abstract: I will give a brief introduction to the classical theory of birational geometry, in particular the minimal model program(MMP). Singularities play a crucial role in birational geometry and MMP. They are often measured by numbers called log discrepancies, and the “worst” type of singularities for which MMP works are called Log Canonical, or LC for short. I will then discuss some recent p...
Scrollar syzygies, scrollar invariants and resolvents Friday, 08.Mar.2019, 13:00--14:00
Abstract: In this talk, we will present some conjectural relations between scrollar syzygy resolution of algebraic curves and the classical theory of resolvents for solving algebraic equations. We will give a Galois theoretic perspective of the syzygy theory. If time permits, some possible number theory applications will also be discussed. This is a joint work with Wouter Castryck.
On the fundamental group of the Galois cover of certain algebraic surfaces 01.03.2019, 13:00--14:00
Abstract: Let X be a surface of degree n, which is considered as a branch cover of CP^2 with respect to a generic projection. The surface X has a natural Galois cover with Galois group S_n. In this talk, we will use Moishezon-Teicher’s method to compute the fundamental group of the Galois cover of certain algebraic surfaces that can degenerate to a union of n projective planes such that no thre...
Time Stepping Schemes for Fractional Diffusion 2019年2月25日下午4:00-5:00
报告摘要: Over the last decade, a large number of time stepping schemes have been developed for time-fractional diffusion problems.

These schemes can be generally divided into: finite difference type, convolution quadrature type and discontinuous Galerkin methods.

Many of these methods are developed by assuming that the solution is sufficiently smooth, which however i...
Reducing Homological Conjectures by n-Recollements 2019年2月20号下午13:30-14:30
摘要: n-recollements of triangulated categories and n-derived-simple algebras are introduced. The relations between the n-recollements of derived categories of algebras and the Cartan determinants, homological smoothness and Gorensteinness of algebras respectively are clarified. As applications, the Cartan determinant conjecture is reduced to 1-derived-simple algebras, and the Gorenstein symmetry ...
Lonely Wolf: The legend of Alexander Grothendieck(孤独的狼:数学大师亚历山大?格罗滕迪的传奇人生) 2019年元月4日 10:00--11:00
报告人简介:李信明(Lee Sin-Min)美国圣荷西州立大学退休教授,从事图论代数与数论研究, 迄今已发表论文200多篇。 著有1-8册的《数学和数学家的故事》(香港?角?出版社,中国新?书局,上海科学技术出版社)、《中国数学五千年》(台湾书局)、《数学家?奇》,《李学数讲数学故事》(九章出版社)、散文《梦裹寻她千百度》,《追虹逐梦的年代》(香港天地图书)

报告内容简介:Prof. A. Grothendieck passed away on No...
Distributed Optimization from Control Perspective 2019-1-2 10:30-11:30
Lihua Xie received the B.E. and M.E. degrees in electrical engineering from Nanjing University of Science and Technology in 1983 and 1986, respectively, and the Ph.D. degree in electrical engineering from the University of Newcastle, Australia, in 1992. He was with the Department of Automatic Control, Nanjing University of Science and Technology from 1986 to 1989. Since 1992, h...
Almost everywhere convergence of averages 2019年1月2日至10日 10:00-11:00
(1) Colloquium : ? In this first talk we shall describe some general principles in the theory of Lebesgue differentiation, see how the validity in general frameworks of a Lebesgue-type differentiation theorem relates to property of some associated operator, before to focus our attention on the delicate issue of differentiating along rectangles ?.

(2) Lectures : ? After recalling so...
Cooperative function 2018-12-28 10:00-11:30
报告摘要:We study a common scenario in industry where returns to scale are nondecreasing and thus full cooperation via pooling all the resources together among related firms is the most efficient way of production. This scenario is usually modelled as a class of cooperative games, referred to as resource pooling games. We argue that resource pooling games could be better understood via directly a...
Motivic multiple zeta values of level two 12月26日10:15-11:15


On the nonabelian Hodge theory 12月26日9:00-10:00
There are two kinds of holomorphic objects on a Kahler manifold: Higgs bundle and flat connection.
The nonabelian Hodge theory extablishes a correspondence between stable(polystable) Higgs bundles and simple(semisimple) flat connections
via the existence of harmonic metric satisfying the Hermitian-Yang-Mills equation.
In this talk I will introduce my work on...
Perverse sheaves on semi-abelian varieties 2018年12月25日(星期二)上午10:00至11:00
摘要:We give a complete (global) characterization of complex perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell's work on perverse sheaves on complex abelian varieties, as well as Gabber-Loeser's results on perverse sheaves on complex affine tori. We apply our results to the study of cohomology jump loci of smooth quasi-projective var...
正特征的代数曲面纤维化 2018年12月18日(星期二)上午10:00至11:00
摘要:在这个报告中,我们首先回顾了具有小奇异纤维数目的特征0的代数曲面纤维化的一些经典结果, 然后我们试图将这些结果推广到正特征。特别我们对于特征小于2g+1的有理直线上的纤维化,构造了具有一条奇异纤维的非常模纤维。我们也试图讨论上述纤维化在亏格1与亏格2上的具体分类。这是我和顾怡博士的合作工作。

Canonically fibered surfaces of general type 2018年12月14日(星期五)下午1:00至2:00
摘要:The canonical map of a surface of general type is called fibered, if its canonical map induces a fibration. Beauville showed that the genus of such a fibration is bounded from above by 5 when the geometric genus is large.
Examples with the genus equal to 2 or 3 have been constructed. Xiao asked whether there exists a surface of general type with large geometric genus, whose canonical...
Real Analogue of Arithmetic K-Theory 2018年12月7日(星期五)下午1:00至2:00
摘要: In 1957, in order to formalize his work on Riemann-Roch theorem, Grothendieck introduced the K-theory in algebraic geometry. In 1959, Atiyah and Hirzebruch constructed the topological K-theory as the real analogue. In 1968, using the topological K-theory, Atiyah and Singer gave a new proof of the famous index theorem as a part of the topological version of the Riemann-Roch theorem. In 1990, ...
Ball quotients and hypergeometric functions 2018年12月6日(星期四)下午1:30至2:30
摘要:It has been a long history, since Schwarz, that one of ways to search for a complex hyperbolic lattice is closely related to understanding the monodromy group of a hypergeometric system. In this talk, I will review the work of Schwarz and Klein on the classical Euler-Gauss hypergeometric functions, as well as the Deligne-Mostow theory on Lauricella hypergeometric functions. Then I will discu...
Semipositivity of line bundles and the growth of cohomology 2018年11月30日(星期五)下午1:00至2:00
摘要:Firstly, we recall Siu and Demailly's proof of Grauert-Riemenschneider conjecture, and explain Berndtsson's refined estimates on the cohomology of semipositive line bundles on compact complex manifolds. Secondly, we discuss two questions on nef and pseudoeffective line bundles given by Demailly and Matsumura analogue to Berndtsson's estimates. In this direction, we introduce a pointview of M...
Braided BiGalois theory and its application to Brauer groups (辫子双Galois理论及其Brauer群应用) 2018-11-27 10:00-11:00
Let $(H, \mathcal{R})$ be a quasi-triangular Hopf algebra or a quantum group, $\mathcal{C}$ the representation category of $H$, which is a braided tensor category. The transmutation of $(H,R)$ is a braided Hopf algebra in the category $\mathcal{C}$. We study the braided autoequivalences of the Drinfeld center $\mathcal{Z(C)}$ which are trivializable on $\mathcal{C}$. To this end, w...
Program for the Mini-Workshop on Hochschild Cohomology and Related Topics III 2018年11月24日-11月25日
Minicourse on matrix factorizations 11月22日上午10:00-11:00, 二教417
11月22日上午10:00-11:00, 二教417
11月22日下午13:30-14:30, 数学楼127

(1) Basics of dg categories.

We review basic notions of dg categories, such as its definition, dg-modules, perfect modules, generators, and so on.

(2) The dg category of matrix factorizations.
Aspects of moduli of curves and polarized varieties 11月21日 (周三),11月23日(周五)下午 2 : 00 - 3 : 30
Abstract: The purpose of the lectures is to explain a few algebraic and complex analytic aspects of moduli spaces. We plan to explain a few problems related to moduli space of Riemann surface, such as metric properties, rigidity of mapping class groups and some results related to conjectures of Coleman and Oort. We are also going to explain the joint work with Wing-Keung To on various hyperbol...
Existence of Symmetric Differentials on Hyperbolic Space forms 11月20日 (周二)下午 3 : 00 - 4 : 00
Abstract: Let $X=\mathbb{B}^n/\Gamma$ be noncompact finite volume quotient of complex unit ball by a torsion-free lattice. Suppose $\overline{X}$ is the Mumford compactification of $X$. We consider the problem of producing symmetric differentials on $\overline{X}$ vanishing at the infinity $D=\overline{X}-X$. These symmetric differentials may be viewed as a generalization of cusps forms on modula...
Algebraic dynamics of automorphism groups in positive characteristic 11月20日 13:30 -14:30
摘要:The dynamics of automorphism groups of normal complex projective varieties (or compact Kahler manifolds) has been well understood in the sense that the whole automorphism groups satisfy the so-called Tits alternative type theorem due to De-Qi Zhang.
  The key ingredients are the cohomological interpretation of the topological entropy by Gromov and Yomdin, the higher dimensional Hodg...
短课程:Introduction to Diophantine Geometry (丢番图几何初步) 2018年11月14日-12月12日

授课人简介:Mounir Hajli于2012年博士毕业于巴黎第六大学,目前任职于上海交通大学。他的主要研究方向为算术几何和Arakelov几何。

Finding Rational Curves by Forgetful Maps 11月14号上午 10:00-11:00
摘要:In this talk, we are mainly concerned with the geometry of rational curves on algebraic varieties. Our main object of study is rationally connected varieties, a kind of varieties that contain “plenty” of rational curves. It was shown by Koll?ar-Miyaoka-Mori that a kind of “smoothing of comb” technique is available on this kind of varieties. We firstly show a most general form of this kin...
Patterson-Sullivan construction for random point processes and the reconstruction of harmonic functions 11月13日(周二),1:30-2:30 pm
摘要: In a recent joint work with Alexander Bufetov, we show that the classical Patterson-Sullivan construction in conformal dynamical system can be generalized to the random setting in the theory of point processes. This construction allows us to recover the value of any harmonic function with additional regularity at any point of the disc from its restriction to a random configuration of the de...
Fano簇的有界性 2018年11月12日下午3点至4点
摘要:这个报告将简介关于Fano簇有界性的BAB猜想,以及Caucher Birkar的工作。通过一些例子介绍证明中的出现的一些新概念,如complements和generalised log pair。这个报告的基础设定在学过 Hartshorne的书。

Lawson同调与周簇 11月12日10:00?11:00
报告人简介: 2006年毕业于美国State University of New York at Stony Brook,导师H. Blaine (Herbert) Lawson, Jr. 现四川大学教授,国家优秀青年基金获得者。
邀请人: 杜荣
Extensions of vertex operator algebras and modular invariants 2018-10-29 14:00-15:00
摘要:In this talk, we will talk about the classification of rational vertex operator algebras. First, we will talk about the background and motivations of our results. Then we will talk about some basic results in the theory of vertex operator algebras. Finally, we will talk about the classification of extensions of some important vertex operator algebras.

Topological entropy of free semigroup actions for noncompact sets 2018-10-29 13:00-14:00
摘要:In this paper we introduce the topological entropy and lower and upper capacity topological entropies of a free semigroup action, which extends the notion of the topological entropy of a free semigroup action defined by Bufetov, by using the Caratheodory-Pesin structure (C-P structure). We provide some properties of these notions and give three main results. The first is the relationship bet...
Numbers with simply normal β-expansions 2018年10月22日, 13:00---14:00
摘要:When β ∈ (1,2) it is well-known that almost every x ∈ [0, 1/(β-1)] has a continuum of β-expansions. In this talk we show that there exists a critical base β_T ≈ 1.80194, the unique zero in (1,2) of the polynomial x^3-x^2-2x+1, such that for β ∈ (1, β_T] every interior point of [0, 1/(β-1)] has a simply normal β-expansion, while for β ∈ (β_T, 2) there exists a point in [0, 1/(β...
Computing a categorical Gromov-Witten invariant 2018-10-18 14:00-15:00
报告内容摘要:We compute the g = 1, n = 1 B-model Gromov-Witten invariant of an elliptic curve E directly from the derived category of coherent sheaves on E. More precisely, we carry out the computation of the categorical Gromov-Witten invariant defined by Costello using as target a cyclic A-infinity model due to Polishchuk. This is the first non-trivial computation of a positive genus categorical...








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