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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.

On the representation of finite W-superalgebras 2020年11月7日10:40-11:40
*主持人:舒斌 教授
*地点:腾讯会议号 845 262 454

A relation between the finite W-superalgebras and finite W-algebras was found in one of my work joint with Bin Shu. This relation turns out to be very useful in the representation theory of finite W-superalgebras. In this talk I first introduce this rel...
Dirac series 2020年12月18日10:00-11:00
*主持人:罗栗 副教授
*地点:腾讯会议 房间号:456 394 627

Let G be a real reductive Lie group. Dirac series of G means the set of all the irreducible unitary Harish-Chandra modules with nonvanishing Dirac cohomology.
After introducing necessary background on Dirac series, I will carefully explain the c...
Chern-Schwartz-MacPherson classes of Schubert cells and applications 2020年12月18日9:00-10:00
*主持人:罗栗 副教授
*地点:腾讯会议 房间号:456 394 627

The Chern-Schwartz-MacPherson (CSM) class is a Chern class theory for singular varieties. In this talk, we will talk about several results about the CSM classes of the Schubert cells. They are related to the Maulik-Okounkov stable bases for the cotangen...
Categorical skew Howe duality and Knot invariants 2020年12月14日、17日
*时间:2020年12月14日8:30---10:30 a.m.
2020年12月17日8:30---10:30 a.m.
*地点:Zoom 会议ID: 941 9680 3264 密码: 122133
Zoom 会议ID: 925 5399 8411 密码: 706922
*主办单位: 华东师范大学数学科学学院
承办单位: 华东师范大学数学科学学院

(1)Introduction to skew Howe duality:
F-manifold algebras and deformation quantization via pre-Lie algebras 2020年12月3日 10:00
主持人:周国栋 副教授
时间:2020年12月3日 10:00

The notion of an F-manifold algebra is the underlying algebraic structure of an F-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding semi-classical limits. We study ...
量子丛代数的Poisson结构与二次量子化 2020年12月1日14:00-15:00
*主持人:胡乃红 教授
*地点:闵行校区数学楼102会议厅 + 腾讯会议ID:281195104 密码:202012

Recent progress of various Volume Conjectures for links as well as 3-manifolds 2020年12月1日(周二) 14:00-15;00
主持人:胡乃红 教授
时间:2020年12月1日(周二) 14:00-15;00
地点:腾讯会议号:831856730 密码:202012

The original Volume Conjecture of Kashaev-Murakami-Murakami predicts a precise relation between the asymptotics of the colored Jones polynomials of a knot in S^3 and the hyperbolic volume of its complement. I will discuss two different directions ...
Reynolds algebras and their free objects from bracketed words and rooted trees 2020年11月18日14:00
*主持人:周国栋 副教授
*地点:腾讯会议 房间号:69989365686 密码:2020

The study of Reynolds algebras has its origin in the well-known work of O. Reynolds on fluid dynamics in 1895 and has since found broad applications. It also has close relationship with important linear operators such as algebra endomor...
3-transportation groups and vertex operator algebras generated by Ising vectors of $\sigma$-type 2020年11月17日14:00
*主持人:焦翔宇 副教授

We give a complete classification and characterization of OZ-type vertex operator algebras generated by Ising vector of $\sigma$-type. Furthermore we prove that all these vertex operator algebras are rational, $C_2$-cofinite and unitary, with which we prove th...
Nilpotent orbits in modular Lie algebras 2020年11月13日15:00-16:00
*主持人:舒斌 教授
*地点:腾讯会议ID:377 588 550

*讲座内容简介:I will survey some works jointly with Bin Shu (and Yunpeng Xue) on nilpotent orbits in enhanced Lie algebras under adjoint action of enhanced algebraic groups. The survey is also involved in some works on nilpotent orbits of Lie algebras of Cartan type. Differ...
模李代数表示中的拟单模 2020年11月13日14:00-15:00
*主持人:舒斌 教授
*地点:腾讯会议ID:377 588 550

Construction of free differential algebras by extending Gr?bner-Shirshov bases 2020年11月11日14:00
*主持人:周国栋 副教授

As a fundamental notion, the free differential algebra on a set is concretely constructed as the polynomial algebra on the differential variables. Such a construction is not known for the more general notion of the free differential algebra on an algebra,...
On the minimal finite W-superalgebras 2020年11月7日9:30-10:30
*主持人:舒斌 教授
*地点:腾讯会议号 845 262 454

In this talk we will consider finite and refined W-superalgebras associated with minimal nilpotent elements, which will be called the minimal ones. We first introduce the explicit generators and their commutators of minimal finite W-superalgebras, and th...
Simplicity of vacuum modules and associated varieties 2020年11月7日8:30-9:30
*主持人:舒斌 教授
*地点:腾讯会议号 845 262 454

We prove that the universal affine vertex algebra associated with a simple Lie algebra $g$ is simple if and only if the associated variety of its unique simple quotient is equal to $g*$. We also derive an analogous result for the quantized Drinfeld-Sokolo...
Auslander-Reiten Conjecture under Singular equivalences 2020年10月30日14:00
*主持人:周国栋 副教授
*地点:腾讯会议ID:94833789018 密码:201030

Auslander-Reiten Conjecture states that the module category of an Artin algebra $A$ admits no finitely generated non-projective module $X$ such that $Ext_A^i(X, A\oplus X)=0$ for all $i>0$. If this holds for all Artin algebra, then t...
BV algebra structures on the Hochschild cohomology of generalized Weyl algebras 2020年10月23日10:00-11:00
*主持人:周国栋 副教授
*地点:腾讯会议ID:824654527 密码:201023

In this talk, we establish the Van den Bergh duality at the level of complex for a class of skew Calabi-Yau generalized Weyl algebras. Then we determine the BV algebra structures on the Hochschild cohomology of these algebras, by virtue ...
Rota-Baxter Lie groups, Rota-Baxter Lie groupoids and algebroids 2020年10月16日09:00-10:00
*主持人:周国栋 副教授

We introduce Rota-Baxter operators on Lie groups so that the differentiation of a Rota-Baxter operator on a Lie group gives a Rota-Baxter operator on the corresponding Lie algebra. The factorization theorem for Rota-Baxter Lie groups are proved. As geomet...
代数 Groebner - Shirshov 基理论的一种新 2020年10月14日 13:00
*主持人:周国栋 副教授
*时间:2020年10月14日 13:00
*地点:腾讯会议ID:770 358 001

1962年,俄罗斯数学家A.I. Shirshov在证明一关系李代数的字问题可解时建立了一套理论方法,现在人们一般称之为李代数的Groebner-Shirshov基理论。在该文中作者利用了李代数的Groebner-Shirshov基与结合代数Groebner-Shirshov基的联系进行证明,因此该证明方法难以...
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...








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