*主持人：周国栋 教授

*讲座内容简介：
Various compatibility conditions among replicated copies of operations in a given algebraic structure have appeared in broad contexts in recent years. Taking an uniform approach, this paper gives an operadic study of compatibility conditions for nonsymmetric operads with unary and binary operations, and homogeneous quadratic and cubic rela...

时间：2018年12月11日（星期二）上午10：00-11：00
　　　2018年12月11日（星期二）下午13：00-14：00
　　　2018年12月13日（星期四）下午13：00-14：00
地点：闵行校区数学楼401报告厅

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

主...

*主持人：舒斌 教授
*时间：2020年11月7日10：40-11：40
*地点：腾讯会议号 845 262 454

*讲座内容简介：
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...

*主持人：周国栋 教授

*讲座内容简介：
In this talk, we establish the cohomology of the relative Rota-Baxter operators on Lie-Yamaguti algebras using the Yamaguti cohomology. Then we use this type of cohomology to characterize the deformations of the relative Rota-Baxter operators on Lie-Yamaguti algebras. We show that if two linear or formal deformations of a relative Rota-Bax...

*主持人：杜荣 教授

*讲座内容简介：
Derived Algebraic Geometry (DAG) allows us to extend Grothendieck's theory of projectivizations and Grassmannians from sheaves to complexes. This extension proves valuable for constructing and studying moduli spaces, especially in the presence of singularities. In this talk, we discuss the construction and properties of derived projectivizat...

*主持人：杜荣 教授

*讲座内容简介：
Geometric quantization on symplectic manifolds plays an important role in representation theory and mathematical physics, deeply relating to symplectic geometry and differential geometry. A crucial problem is to understand the relationship among geometric quantizations associated with different polarizations. In this talk, we will discuss th...

*主持人：胡乃红 教授

*讲座内容简介：
We will discuss a general construction of the Sugawara operators for the quantum affine algebra of type A. In 2016, we gave an explicit construction of the Sugawara operators in terms of certain traces over a tensor products associated with antisymmetrizers of the Hecke algebra. In this talk, we generalize the construction and construct ce...

*主持人：罗栗 教授

*讲座内容简介：
In this talk, we present some studies of elementary abelian p-subgroups of algebraic groups and applications in the Inverse Galois problem, the classification of acceptable Lie groups, the Alperin weight conjecture, etc.

*主讲人简介：
余君，北京大学副教授，2012年在苏黎世联邦理工大学获得博士学位，主要从事李群的表示理论研...

*主持人：陈苗芬 教授

*讲座内容简介：
In this talk, I will formulate the anticyclotomic Iwasawa main conjecture for Rankin-Selberg products of automorphic representations of hermitian type, and state our results. I will then explain the main ingredients of the proof: an Ihara type lemma, Abel-Jacobi image of basic locus, and a bipartite Euler system over the Iwasawa algebra. T...

*主持人：孟晟 研究员

*讲座内容简介：

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.

*主讲人简介：

冀诸超...

*时间：9月18日8：30-10：00，19日8：30-10：00，21日13：00-14：30
*地点：数学楼126
*主持人：周国栋 教授

*讲座内容简介：
Geometric surface models in the representation theory of finite dimensional algebras have their origin mainly in the theory of cluster algebras and their categorifications. In particular, the representation theory of a class of quadratic monomia...

*主持人：周国栋 教授

*讲座内容简介：
In this mini-course, the deformation theory of Ginzburg Calab-Yau algebras is related to negative cyclic homology. We do this by exhibiting a DG-Lie algebra that controls this deformation theory and whose homology is negative cyclic homology. We show that the bracket induced on negative cyclic homology coincides with Menichi's string topo...

*主持人：罗栗 教授

*讲座内容简介：

I will discuss a proof of a conjecture of almost twentyyears on the modular invariance of (logarithmic) intertwining operators.Let V be a C_2-cofinite vertex operator algebra without nonzero elements of negative weights. The conjecture states that the vector space spanned by pseudo-q-traces shifted by -c/24 of products of (logarithm...

*主持人：胡乃红 教授

*讲座内容简介：

I will discuss recent joint work with X. Huang, H. Xu and Y. Zhi on certain new geometric characterizations of complex projective space using p-form spectra and Bergman kernel.

*主讲人简介：

刘克峰，国际著名数学家、美国加州大学洛杉矶分校数学教授、浙江大学数学科学中心执行主任、浙江大学首位光彪讲座教授、...

*主持人：罗栗 教授

*讲座内容简介：

报告人将根据自己从事雅可比猜想研究18年的经历，总结出来的用代数、几何和分析等基础数学方法的有效结合，给出二维雅可比猜想的证明。这一方法被雅可比问题专家Zbigniew Hajto称为“can be useful in affine algebraic geometry”。在这个报告中，报告人将侧重讲述如何有效利用代数和分析给出多项式映射在无穷远点处的一个重要性质，该性质在二维雅可比猜想的证...

*主持人：罗栗 教授

*讲座内容简介：

The coadjoint orbit method of Kirillov and Kostant suggests that irreducible unitary representations of a Lie group can be constructed as quantization of coadjoint orbits of the group, which was later reformulated by Vogan in algebro-geometric language for noncompact reductive Lie groups. I will propose an approach to this conjecture...

*主持人：罗栗 教授

*讲座内容简介：
We characterize simple smooth modules over some infinite-dimensional Z-graded Lie algebras. More precisely, we prove that if one specific element of a Z-graded Lie algebra L locally finitely acts on a simple L-module V, then V is a smooth L-module. These infinite-dimensional Z-graded Lie algebras include the Virasoro algebra, affine-Virasoro...

*主持人：罗栗 教授

*讲座内容简介：

Let G be a simply connected semisimple group of rank rover an algebraically closed field. Steinberg has associated to each minimal length Coxeter element an r-dimensional affine space in G,which is a cross-section of all regular conjugacy classes of G. In this talk, we will consider natural analogues of Steinberg’s cross-sections in...

*主持人：罗栗 教授

*讲座内容简介：

In this talk, we introduce the theory of regular representations of Mobius quantum vertex algebras. Assuming that Mobius quantum vertex algebra V satisfies certain suitable conditions, we obtain a Mobius weak quantum vertex algebra V\otimes V with a nonzero complex z as the parameter. Using this result, we construct a family of V^{op...

*主持人：罗栗 教授

*讲座内容简介：

We characterize indecomposable objects, and give a simple formula for the Auslander–Reiten translation in the monomorphism category Mono(X).

*主讲人简介：

高楠，上海大学数学系教授、博导，上海市东方学者特聘教授。 研究领域为代数表示论，三角范畴，导出范畴，Gorenstein同调代数。已在Comm.Contem.Math.、J.Algeb...

*主持人：罗栗 教授

*讲座内容简介：

Let N be a normal subgroup of a finite group G and V be a fixed finite-dimensional G-module. The Poincare series for the multiplicities of induced modules and restriction modules in the tensor algebra T(V)=⊕_{k≥0}V^{?k} are studied in connection with the McKay-Slodowy correspondence. In particular, it is shown that the closed formu...

*主持人：罗栗 教授

*讲座内容简介：

In this talk, I give a brief introduction to some new developments in systems of matrix equations and tensor equations.

*主讲人简介：

王卿文，上海大学二级教授、伟长学者特聘教授、上海领军人才。现任中国高等教育学会教育数学专业委员会理事长、多个国际数学期刊的主编及编委。获宝钢优秀教师奖、王宽诚育才奖、上海市...

*主持人：杜荣 教授

*讲座内容简介：

A theorem of Ein, Lazarsfeld, Smith and Varolin gave a connection between jumping numbers of multiplier ideals and roots of Bernstein-Sato polynomials of a regular function. I will first talk about a generalization of multiplier ideals, i.e. Hodge ideals, and give an explicit computation of Hodge ideals for some special types of hype...

*主持人：罗栗 教授

*讲座内容简介：

Recently, Baumann-Kamnitzer-Knutson introduced a remarkable algebra morphism: \bar{D} from C[N] to the field of rational functions C(a_1, ..., a_n), where N is the unipotent radical of a simply laced complex algebraic group and a_i are simple roots, in their proof of a conjecture of Muthiah about MV basis of C[N]. The algebra C[N] an...

*主持人：周国栋 教授

*讲座内容简介：

In this talk, we will compare the representations, symplectic structures, relative Rota-Baxter operators and the cohomology theory of Lie algebras and the 3-Lie algebras induced by Lie algebras with quasi-trace functions. We introduce a notion of a quasi-trace function on a pre-Lie algebra, which can be used to construct a 3-pre-Li...

*主持人：罗栗 教授

*讲座内容简介：

陈良云，东北师范大学数学与统计学院三级教授、博士生导师、博士后合作导师。南开大学理学博士、哈尔滨工业大学博士后、东京大学博士后。吉林省拔尖创新人才、吉林省教育厅新世纪优秀人才、长春市有突出贡献专家，省级精品课负责人。主要研究方向是李超代数及其应用，主持国家自然科学基金科研项目五项、省部级科研项目六项，主研国家面上项目三项，发表110余篇...

主持人：胡乃红 教授

报告内容简介：
Quantum affine algebras are quantum enveloping algebras of affine Lie algebras, introduced independently by Drinfeld and Jimbo in their study of the Yang-Baxter equation. Representation theory of quantum affine algebras depends mostly on the Drinfeld realization,

which was announced in 1987. Ding and Frenkel proved the present...

*主持人：舒斌 教授（会议密码请与舒斌老师联系）

*讲座内容简介：
In this talk, I will introduce the super Yangian Y(m|n) associated to the general linear Lie superalgebra gl(m|n) over a field of positive characteristic. We extend Drinfeld-type presentations of Y(m|n) and the special super Yangian SY(m|n) to positive characteristic. Moreover, the center Z(Y(m|n)) of Y(m|n) is de...

*主持人：舒斌 教授（会议密码请与舒斌老师联系）

*讲座内容简介：
In this talk, I will introduce the Verma modules for finite W-superalgebra U(g,e) associated with a minimal even nilpotent element, and give a complete isomorphism classification of irreducible modules. Those Verma modules can be further described via parabolic induction from Whittaker modules for osp(1|2) or sl(2...

*主持人：舒斌 教授（会议密码请与舒斌老师联系）

*讲座内容简介：
Let g be a basic classical Lie superalgebras over an algebraically closed field of p>2, and U_0(g) the restricted enveloping algebra of g. In this talk, we show a U_0(g)-module is projective if and only if it has both a baby Verma module filtration and a twist baby Verma module filtration. Then we show a Humphrey...

*主持人：周国栋 教授

*讲座内容简介：

Let R be a commutative domain with 1. In this paper, 1-w-cotorsion modules and strongly w_∞-flat modules are introduced and studied. It is shown that an integral domain R is a PVMD if and only if 1-w-cotorsion R-modules are injective if and only if all 1-w-cotorsion R-modules are w-FP-injective. And we show that all w_∞-Matlis co...

*主持人：周国栋 教授

*讲座内容简介：
Recall that a ring R is semisimple (resp.pure semisimple) if R is both left and right semisimple (resp. pure semisimple). Here R is left semisimple (resp. left pure semisimple) if all left R-modules are projective (resp. pure projective). Equivalently, if all left R-modules are injective (resp. pure injective). right semisimple(resp.right ...

*时间：2022年05月24日、26、31日和06月02日 20:30-22:30
*地点：Zoom：957 7669 8134
*主持人：罗栗 教授

*讲座内容简介：
iQuantum groups arise from quantum symmetric pairs and can be viewed as a vast generalization of Drinfeld-Jimbo quantum groups. Various fundamental constructions on quantum groups have been generalized to the setting of i-quantum groups. In this m...

*主持人：周国栋 教授

*讲座内容简介：
In this talk, we introduce the representations and cohomologies of differential 3-Lie algebras with any weight. Deformations and abelian extensions of differential 3-Lie algebras are interpreted by using lower degree cohomology groups. We also characterize the relationship between the cohomologies of a differential 3-Lie algebra and its as...

*主持人：胡乃红 教授

*讲座内容简介：
In the talk we will survey constructions of recollements of derived module categories. This is done by introducing exact contexts and their noncommutative tensor products. Special cases of exact contents are Milnor squares and extensions of algebras. Employing exact contexts, we construct universal localizations and characterize the homolo...

*主持人：周国栋 教授

*讲座内容简介：
Let M be a manifold, E=TM+T*M and C(E) be the Clifford bundle. The differential forms on M is the spin representation of C(E). The Lie bracket on sections of TM can be extended to sections of the bundle E by defining {e_1,e_2}=[[d,e_1],e_2], where both sides are viewed as operators on differential forms and d is the de-Rham differential op...

*主持人：胡乃红 教授

*讲座内容简介：

11.10 19:00---20:00 腾讯会议：664 349 812
Title: Simple non-weight representations of affine Kac-Moody algebras
Abstract: Let H be a Cartan subalgebra of an affine Kac-Moody algebra without containing the center. We determine all simple modules on the polynomial algebra C[H] for all affine Kac-Moody algebras. Can we c...

*主持人：周国栋 教授

*讲座内容简介：

For an integrable distribution $F$ in a smooth manifold $M$, we study the Hochschild cohomology of the dg manifold $(F[1],d_F)$ and establish a canonical isomorphism with the Hochschild cohomology of the transversal polydifferential operators of $F$. In particular, we prove that the Hochschild cohomology of the dg manifold associat...

*主持人：周国栋 教授

*讲座内容简介：
Given a pair of (real or complex) Lie algebroid structures on a vector bundle A (over M) and its dual A?, we find a line bundle L such that there exist two canonically defined differential operators d and d' on Γ(∧A?L). We prove that the pair (A,A?) constitutes a Lie bialgebroid if and only if the square of D=d+d' is the multiplication...

*主持人：周国栋 教授

*讲座内容简介：
Ladders of recollements of abelian categories are introduced, and used to address three general problems. Ladders of a certain height allow to construct recollements of triangulated categories, involving derived categories and singularity categories, from abelian ones. Ladders also allow to tilt abelian recollements, and ladders guarantee ...

*主持人：胡乃红 教授

*讲座内容简介：
量子力学的对称性主要由有限维单李代数的表示来体现。而李代数的微分算子表示无疑更易被物理学家理解和应用。本报告将综述有限维单李代数的典型微分算子表示并介绍我们在这方面的部分工作。其中，沈光宇先生引进的“混合积”和我们求偏微分方程多项式解的基本引理起着重要作用。

*主讲人简介：
徐晓平，中国科学院大学教授。1992年在美国Rutger...

*主持人：胡乃红 教授

*讲座内容简介：
苏育才，同济大学数学科学学院特聘教授、二级教授、博士生导师、同济大学数学研究所所长。国家杰出青年基金获得者、中国科学院“百人计划”入选者、教育部“跨世纪优秀人才”入选者、国务院政府特殊津贴专家、上海市优秀学术带头人、国家自然科学基金重点项目主持人、教育部自然科学二等奖（第一完成人）、上海市自然科学二等奖（第二完成人）、安徽省自然科学二等奖（...

*主持人：胡乃红 教授

*讲座内容简介：
在此报告中，我们将介绍 Tits-Kantor-Koecher构造和一个小的TKK的例子，并构造其量子化。

*主讲人简介：
郜云，加拿大York大学教授、德国洪堡学者。主要研究方向是无穷维李(超)代数、量子群和表示理论。在高维仿射李代数研究领域做出了系列重要工作，在国际一流数学杂志上发表论文50余篇，其中包括两本美国数学会专著(Memoirs of AmericanMathe...

*主持人：胡乃红 教授

*讲座内容简介：
报告中我们将会探讨格顶点代数积分形式的格结构并说明一般顶点算子的除幂会保持由划分-值函数指标的 Schur 函数张成的积分格。我们还将说明 Garland 算子，对应于仿射李代数中 Heisenberg 元素的除幂，也保持该积分形式。这些看法类似于单李代数的包络代数的 Kostant 整形式以及格顶点代数下的代数仿射李群。

*主讲人简介：
景乃桓，美国北卡州...

*主持人：罗栗 副教授

*讲座内容简介：
Tensor structure on the representation category of affine Lie algebras plays an important role in representation theory of affine Lie algebras. In a series of work, Kazhdan and Lusztig constructed rigid braided tensor categories of affine Lie algebras at non-positive rational levels, Huang and Lepowsky gave modular tensor category structur...

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We will talk about various building blocks of vertex operator algebras, and some recent progress in this respect.

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Toroidal extended affine Lie algebras (EALAs) are a class of important EALAs. In this talk we deal with the classification of irreducible integrable modules for toroidal extended affine Lie algebras with any nullities.

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This talk involves some works about the Schur-Weyl-Sergeev duality and its quantum case. Based on the realization of the universal enveloping superalgebra of the queer Lie superalgebra q_n via queer Schur superalgebras, we achieve the integral Schur-Weyl-Sergeev duality. In order to reconstruct the quantum supergroup U_q(q_n) associa...

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????????????????????????2006?????????????????????????????????????????????????????氨?...

*主持人：周国栋 教授

*讲座内容简介：
In this talk, I will introduce two tools for studying the Gorenstein flat dimension: flat-cotorsion theory and Frobenius pairs, also known as Auslander-Buchweitz contexts. Some applications will be given. This talk is based on a joint work with L. W. Christensen, S. Estrada, P. Thompsom, D.-J. Wu and G. Yang..

*主讲人简介：<...