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中俄数学中心——吉大论坛(Sino-Russian Mathematics Center-JLU Colloquium)

Kahler-Ricci flow on smooth minimal models 

 

Speaker:张振雷(首都师范大学)

Time20220701 10:00-12:00

Meeting ID腾讯会议 ID:780-765-137

点击链接入会,或添加至会议列表:https://meeting.tencent.com/dm/5cjuobQFgOpb 

AbstractIt is a survey talk on the long time behavior of a Kahler-Ricci flow on smooth manifold with semi-ample canonical line bundle.

Bio张振雷,首都师范大学数学科学学院教授。2003年本科毕业于吉林大学数学科学学院;2008年博士毕业于南开大学陈省身数学研究所,导师方复全教授。2018年获国家自然科学基金杰出青年科学基金资助主要研究Ricci流、Kahler-Ricci流。

奇妙的基础数学

Speaker:徐晓平中国科学院大学

Time20220624 14:00-16:00

Meeting ID:腾讯会议 ID:703-956-224

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Abstract这是一个科普型报告。我们从“什么是数学”谈起。然后是:素数的故事,拉马驽金的故事,分隔函数,KdV方程,量子物理的基本数学模型。之后,我们讲:数学的残缺美,一些挑战性问题以及本人的一些研究体验。

Bio徐晓平,中国科学院大学教授,中国科学院数学研究所所长。1992年在美国Rutgers大学取得博士学位,师从著名的李理论专家James Lepowsky Robert Lee Wilson。之后在香港科技大学工作十年。2002年回到中国科学院数学研究所工作, 2014年开始兼任中国科学院大学教授,自20223月起,任中国科学院数学研究所所长。获宝钢优秀教师奖。他在李代数、顶点算子代数(共形场论)和偏微分方程的代数解法等相关领域的研究中做出了重要贡献。

低维拓扑学的世纪回顾

Speaker:雷逢春大连理工大学

Time20220624 10:00-12:00

Meeting ID685-963-603

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Abstract拓扑学是当代核心数学的一个重要前沿领域,其渊源可追溯到欧拉早期的工作(1836年,哥尼斯堡七桥问题的解答)。拓扑学奠基于19世纪末, 20世纪取得了梦幻般的发展, 进入21世纪更加兴旺发达。本报告将对拓扑学的发展作一个跨越世纪的通俗概要浏览, 重点介绍低维拓扑学的发展,即二、三和四维流形拓扑学的主要成就。

Bio雷逢春,199012月博士毕业于吉林大学基础数学专业,研究方向为低维拓扑,现为大连理工大学数学科学学院教授、博士生导师。长期从事三维流形拓扑方面的研究工作,多次承担国家自然科学基金面上项目、重点项目和海外及港澳学者合作研究基金(延续)项目的研究工作。曾于1997年荣获国家教委科技进步二等奖(排名3)2001年获黑龙江省杰出青年科学基金,2002年入选教育部“跨世纪优秀人才培养计划”。现为中国数学会常务理事,辽宁省数学会副理事长,大连市数学学会理事长。

Factorization of Shapovalov elements 

Speaker:Andrey MudrovMoscow Institute of Physics and Technology and University of Leicester

Time20220617 15:00-17: 00

Meeting ID:ZOOM ID:862 062 0549, Password:2022

AbstractA classical result of J. Bernstein, I. Gelfand and S. Gelfand says that a singular vector in a Verma module over a simple complex Lie algebra can be obtained from its highest vector by applying a product of special elements of the negative nilpotent subalgebra called Shapovalov elements. We provide explicit formulas for those elements, and hence for singular vectors of the Verma modules, expressing them through certain matrix elements of the inverse contravariant Shapovalov form.

BioThe speaker is currently an Associate Professor and a Senior Researcher at the Center of Fundamental Mathematics in MIPT, and an Honorary Lecturer at the University of Leicester. He is specializing in quantum groups, deformation quantization and related topics. 

关于最对称的双曲环面上的闭测地线

Speaker:张影(苏州大学)

Time20220610 10:00-12:00

Meeting ID564-626-700 

Join to Tecent Meetinghttps://meeting.tencent.com/dm/p7VBNfhblItm

Abstract在与李祥飞的合作工作中,我们研究具有最大对称性的完备的双曲环面上的闭测地线的性质,证明一般闭测地线的迹多项式的正性,一些简单闭测地线长度的单调性,并提出简单闭测地线的迹的凸性猜测,以及一般闭测地线的迹多项式系数的对数凹性猜测。

Bio张影,1985.9-1999.5 吉林大学数学系本研学习、任教,1999.5-2004.7 新加坡国立大学读研,2006.3-2007.2 巴西国家数学所(IMPA)博士后,2009.6至今,苏州大学数学科学学院教授。从事几何拓扑学研究。

同调论简史 

Speaker:段海豹 (中国科学院数学与系统科学研究院)

Time2022527 10:00-12:00

Meeting ID899-680-387

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Abstract同调论是20世纪数学所诞生的一项新技术,是当代几何、拓扑、分析学的有力工具。报告通过 Riemann, Poincare, Brouwer, Hopf 等开拓者们的相关工作介绍,回顾同调论的背景、起源、以及发展历程。

Bio段海豹,中国科学院数学与系统科学研究院研究员,19773月-19851月,在吉林大学数学系学习,获理学学士、硕士学位;19877月,在北京大学获博士学位。从事代数拓扑,微分拓扑和代数几何的教学、研究工作。 他在2005年获中国数学会陈省身数学奖,2010年获国家自然科学二等奖。

Lie 2-algebras from geometric structures 

Speaker:Zhangju LIU

Time2022.5.13 14:00-16:00

Meeting ID347-371-151

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AbstractThe notion of Lie 2-algebras is introduced as categorification of Lie algebras, Which is one of the fundamental objects in higher Lie theory and has close connection with strongly homotopy Lie algebras. The Lie 2-algebra structure has enjoyed significant applications in both geometry and mathematical physics. Strict Lie 2-algebras are equivalent to Lie algebra crossed modules, which are classified by the third cohomology of a Lie algebra.

In this talk, we’ll review several Lie 2-algebras that come from geometric structures, namely, 2-plectic manifolds; Courant algebroids; homotopy Poisson manifolds and affine structures on Lie groupoids. A 2-plectic structure on a manifold is a nondegenerate closed 3-form. There is a Lie 2-algebra structure on functions and Hamiltonian 1-forms of a 2-plectic manifold A Courant algebroid is a vector bundle together with a bilinear form, a skew-symmetric bracket and an anchor map. The bracket satisfies the Jacobi identity up to a coboundary, which generates a Lie 2-algebra on the section space of the bundle and functions on the base manifold. Parallel to the fact that there is a one-to-one correspondence between Lie algebra structures on a vector space and linear Poisson structures on the dual space, there is a one-to-one correspondence between Lie 2-algebra structures on a 2-vector space and linear homotopy Poisson structures on the dual 2-vector space. On a Lie groupoid, vector fields that are compatible with the groupoid multiplication are called multiplicative. Multiplicative vector fields with the Schouten bracket form a Lie algebra, which is not invariant under the Morita equivalence of Lie groupoids. To define vector fields on a differentiable stack, one needs to extend the Lie algebra to a Lie 2-algebra formed by affine vector fields on a Lie groupoid, which is Morita invariant.

Bio刘张炬,北京大学/河南大学教授,19821月本科毕业于吉林大学,19866月在北京大学获得博士学位。1999年获得国家杰出青年基金。主要从事数学物理、Poisson几何等领域的研究。曾入选教育部跨世纪优秀人才支持计划,2004年获得教育部自然科学一等奖。

Morse matching method for conformal cohomology 

Speaker:Pavel Kolesnikov (Sobolev Institute of Mathematics)

Time2022.5.6 10:00-12:00

Meeting ID862 062 0549

Password:2022

Join to Zoom Meetinghttps://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09

AbstractWe will observe the matching method in the algebraic discrete Morse theory which provides us a powerful tool for finding Anick resolutions for associative algebras defined by generators and relations. We apply this method to find reduced Hochschild cohomologies of associative conformal algebras in order to study their relations with the cohomologies of Lie conformal algebras. In particular, we evaluate the Hochschild cohomology groups for the universal associative envelope U(3) of the Virasoro Lie conformal algebra.

BioPavel Kolesnikov got his PhD in 2002 in Novosibirsk State University (NSU) and joined Sobolev Institute of Mathematics. Now he is a research fellow of the Institute and professor in the NSU. His main area of research interests is in the structure and combinatorial theory of associative and non-associative algebras, conformal and vertex algebras.

 

On the cobar-construction for non-simply connected spaces

Speaker:Andrey Lazarev ( Lancaster University )

Time:2022.04.22 16:00-18:00

Meeting ID862 062 0549

Password2022

Join to Zoom Meetinghttps://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09

AbstractThe cobar-construction produces a differential graded (dg) algebra out of a dg coalgebra. When applied to the coalgebra of simplicial chains on a simply-connected space X, the resulting dg algebra models the chain algebra on the based loop space of X. This is a classical result of Adams and it has been known for over 60 years. In a recent breakthrough development, American mathematicians Rivera and Zeinalian removed the simple-connectivity assumption.  In this talk, I will explain Rivera-Zeinalian’s result, discuss its generalizations and connections with infinity-categories.

BioAndrey Lazarev is a professor of pure mathematics in the University of Lancaster. His recent research deals with homotopy theory of differential graded algebras and categories, derived categories and higher phenomena. It has applications in rational homotopy theory, theory of operads and operadic algebras, algebraic topology and pure algebra. Andrey Lazarev is the Managing Editor of the journalBulletin of the London Mathematical Society》, as well as a Member of the Editorial Board of  the journalHigher_Structures》.

 

Boson-Fermion Correspondence and Its Applications to Integrable Hierarchies Revisited From The Point of View of Representation Theory and Random Walks

Speaker:Jian Zhou

Time2022.04.15 10:00-12:00

Meeting ID694-475-243

Join to Meetinghttps://meeting.tencent.com/dm/dbl4pDJLd3zS

AbstractWe revisit the boson-fermion correspondence and its applications to integrable hierarchies via representation theory of symmetric groups. This makes it natural to consider random walks on various diagrams and graphs related to symmetric groups. Random partitions, hypergeometric tau-functions and weighted Hurwitz numbers are then brought together under a unified probabilistic treatment, rooted in their connections to the fermionic Fock space. Various approaches to the representation theory of symmetric groups all turn out to be useful in this treatment. They include: the new approach of Okounkov and Vershik, the Hopf algebra approach of Zelevinsky, and the lambda-ring approach of Knutson. A connection to the interpolating statistics in the study of fractional quantum Hall effect will also be explained.

Bio周坚,清华大学数学科学系教授,2005年国家杰出青年基金获得者、2009年入选国家“百千万人才工程”。他的研究领域为黎曼面的模空间与霍奇积分,拓扑场论,微分几何,弦理论等。周坚教授通过对超弦理论中Vafa学派的工作中出现的一些数学问题的研究,揭示了一些不同的数学分支之间的内在联系,他与合作者完成的“Marino-Vafa猜想的证明”入选2004年度“中国高校十大科技进展”。

Heegaard splitting: a survey

Speaker:邱瑞锋 (华东师范大学)

Time:2022年04月08日 10:00-12:00

Meeting:#腾讯会议:680-593-921

https://meeting.tencent.com/dm/lxemeq0TOyx1

Abstract: Heegaard分解是紧致三维流形上普遍存在的组合拓扑结构,在三维流形理论的研究中起到了重要的作用。吉林大学是我国最早从事这一领域研究的研究群体,并直接或间接地培养了一批这一领域的专家学者。这个报告将介绍这一领域的国内外发展历史及现状。

Bio:邱瑞锋,华东师范大学教授,主要从事三维流形及纽结理论的研究,代表性工作有:(1)证明了Heegaard分解理论中的Gordon猜想,(2)构造了纽结洞数理论中的Morimoto猜想的反例等。

 

Orbifold theory and modular extensions
 

Speaker: 董崇英 美国加州大学Santa Cruz 分校

Time:2022-03-25 10:00-12:00 

Abstract: Orbifold theory studies a vertex operator algebra V under the action of a finite automorphism group G.  The main objective is to understand the module category of fixed point vertex operator subalgebra V^G.  We prove a conjecture by Dijkgraaf-Pasquier-Roche on V^G- module category if V is holomorphic. We also establish a connection between rational orbifold theory and minimal modular extensions. Our work is based on the previous results on modular extensions by Drinfeld-Gelaki-Nikshych-Ostrik and Lan-Kong-Wen. This is a joint work with Richard Ng and Li Ren.

Bio: 董崇英,美国加州大学Santa Cruz分校终身教授,国际上无限维李代数和顶点算子代数领域最杰出的数学家之一,多年来一直从事无穷维李代数、顶点算子代数、Orbifold理论以及广义月光等方面的研究。在Acta Math.、Duke Math. J.、Adv. Math.、Comm. Math. Phys.等国际著名期刊发表论文100多篇,总引用超过3000次,其中包括菲尔兹奖获得者Drinfeld、Zelmanov和Borcherds以及著名数学家如Beilinson和Kac等人的重要引用。主持多项美国自然科学基金,并担任杂志Algebra Colloquium的主编以及Science China Mathematics等多个杂志的编委。
Meeting:128-767-072加入会议:
https://meeting.tencent.com/dm/hyMIOAPeEsWf

Deformations of Symplectic Foliations

Speaker: Marco Zambon (KU Leuven)

Time: 2022.03.04  20:00-22:00

Location: Zoom 

          ID:862 062 0549

          Password:2022

Meeting:https://us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09

Abstract:

Symplectic foliations and regular Poisson structures are the same thing. Taking the latter point of view, we exhibit an algebraic structure that governs the deformations of symplectic foliations, i.e. which allows to describe the space of symplectic foliations nearby a given one.  Using this, we will address the question of when it is possible to prolong a first order deformation to a smooth path of symplectic foliations. We will be especially interested in the relation to the underlying foliation. This is joint work with Stephane Geudens and Alfonso Tortorella.

Bio:

Marco Zambon is an associate professor at KU Leuven, Belgium. He works on topics related to Poisson geometry, in particular on those related to foliations, deformations and Lie theory.

 

 

Diophantine approximations

SpeakerNikolay Moshchevitin (Moscow State University)

Location:Zoom

           ID:894 9789 1576

          Password237198

Lecture1. Continued fractions.
2022.01.19, 13:30-15:00

Representation of real numbers as continued fractions. Approximation by convergents, Perron's formula.
Irrationality measure function.
Lagrange and Dirichlet spectra. Minkowski diagonal continued fraction and the related spectrum. Geometry of continued fractions algorithm.


Lecture2. Distribution of Farey fractions.
2022.01.20, 13:30-15:00

Elements of basic number theory. Euler and Moebius functions.
Integral representation of greatest common divisor. Counting the number of reduced fractions in [0,1].
Fraenel's theorem. Relation to Riemann zeta-function.


Lecture3. Farey tree and Minkowski function.
2022.01.26, 13:30-15:00

Stern-Brocot sequences. Minkowski question-mark function.
Salem's theorem on the derivative. Fixed points problem. An analog to Fraenel's theorem.
Fourier-Stieltjes coefficients.


Lecture4.Multidimensional approximation.
2022.01.27, 13:30-15:00

Simultaneous approximation to real numbers. Linear forms close to xero.
Basic laws of approximation. Best approximations and phenomenon of degeneracy of dimension.
Diophantine exponents and Jarnik's inequalities.

Bio: Nikolay Moshchevitin教授现就职于莫斯科国立大学,研究兴趣为Geometry of numbers, geometric theory of Diophantine approximations, ergodic and combinatorial theory of numbers, theory of dynamical systems。共发表论文70余篇,超过400次引用。于1998年获得俄罗斯联邦国家奖

 

Geometry of Gaussian random curves

SpeakerAndrey Dorogovtsev(Institute of Mathematics,NAS Ukraine)

Location:Zoom

          ID:858 7772 7123

         Password:803617

Abstract:

This course aims to provide a solid introduction on the geometry of Gaussian random curves. Since the theory of geometry of Gaussian random curves is based on the concept of Gaussian random process and fields, the first part of the course will be devoted to some properties of this process and fields. And the second part of the course is devoted to discussion of geometry of Gaussian random curves like the Self-intersection local times for planar Brownian motion and the hitting probabilities for planar Broownian motion. Professor Andrey will give students some time to understand the knowledge and give some small questions about the lecture.

Time:

 

Lecture 1: Gaussian random processes and fields. Main examples

In this lecture we give the definition of Gaussian random processes and fields. Also, we will give some examples to understand this.

Lecture 2: Smoothness of Gaussian random fields

In this lecture we discuss the smoothness of Gaussian random fields, and we can get some properties on Gaussian random fields.

Lecture 3: Euler characteristic of the subsets in Euclid space

In this lecture we give the definition of Euler characteristic which in defined on Euclid space, it is topological invariant.

Lecture 4: Rice formula and asymptotic of tales for supremum of Gaussian random fields

In this lecture we give the Rice formula and discuss the asymptotic of tales for supremum of Gaussian random fields.

Lecture 5: Trajectory of Brownian motion as a random curve. Basic properties

In this lecture we discuss the trajectory of Brownian motion and give some basic properties about this.

Lecture 6: Self-intersection local times for planar Brownian motion

In this lecture we discuss the investigation of the local times of self-intersection as the most important geometric characteristics for planar Brownian motion.

Lecture 7: Hitting probabilities for planar Brownian motion

In this lecture we discuss the hitting probabilities and how we use this to describe the trajectory of planar Brownian motion.

Lecture 8: Tube formula for planar Brownian motion

In this lecture we give the Tube formula for planar Brownian motion, and use it to help us learn the trajectory of Brownian motion.

Bio:

Andrey Dorogovtsev教授是乌克兰国家科学院通讯院士,乌克兰国家科学院数学所随机过程理论系主任,主要从事概率论及其相关领域研究,是乌克兰概率论研究方向学术领军人物之一。Andrey Dorogovtsev教授是乌克兰与德国、乌克兰与俄罗斯等国家联合项目的乌方负责人。同时,Andrey Dorogovtsev教授是《Theory of Stochastic Processes》、《Ukraine Mathematical Journal》等杂志的编委。

 

Knot theory

SpeakerVassily Olegovich Manturov(Moscow Institute of Physics and Technology)

Time:2022年1月

LocationTencent Meeting             

               Room Number:614-9548-1864 

                 Password:372633

Abstract: 

Lecture1. 

Reidemeister moves. Colouring invariants, and the linking number.

2022/01/06 18:00-19:00

Abstract:

We will introduce diagrams of knots and links. We use the diagrams to build two invariants of links: Coloring invariant and the linking number.

 

Lecture2. 

The Kauffman bracket, the Jones polynomial.

2022/01/09 18:00-19:00

Abstract:

We will use Kauffman bracket to prove that Jones polynomial is a link invariant.We will compute some examples and prove the Kauffman-Murasugi-Thistlethwaite Theorem.

 

Lecture3.  

Fundamental group. The knot group.

2022/01/13 18:00-19:00

Abstract:

We will define a famous link invariant: the fundamental group of the knot complements. We will show that this group is not trivial if the knot is not trivial.

 

Lecture4. 

The knot Quandle is a complete knot invariant.

2022/01/16 18:00-19:00

Abstract:

Matveev and Joyce defined a knot invariant, the knot quandle.  This is a complete invariant. We can obtain many invariants from the knot quandle, for example, the knot group and coloring invariant.

 

Lecture5.  

The braid groups

2022/01/20 18:00-19:00

Abstract:

We define the braid group. The action of the braid group on Aut(F_{n}) is complete.We will also discuss Markov Theorem and Alexander Theorem.

 

Lecture6.  

The Alexander polynomial.

2022/01/23 18:00-19:00

Abstract:

We will introduce several ways to define the Alexander polynomial.

 

Lecture7.  

Vassiliev invariant

2022/01/27 18:00-19:00

Abstract:

We will introduce the Vassiliev invariant and prove that “polynomial” invariant are all come from the Vassiliev invariant.

 

Lecture8.  

Khovanov homology

2022/01/30 18:00-19:00

Abstract:

Khovanov homology is a categorification of the Jones polynomial, in the sense that its Euler characteristic is the Jones polynomial.

 

Bio:Professor Vassily Olegovich Manturov is from Moscow Institute of Physics and Technology. His research interest is low dimensional topology and knot theory.  He has published more than 150 papers and got more than 1500 citations. He got "Professor of RAS" in 2016 and he is one of the Managing Editors of the "Journal of Knot Theory and Its Ramifications". He has published many books, for instance, 《Parity in knot theory and graph-links. Contemporary Mathematics. Fundamental Directions》,《Low-dimensional Topology and Combinatorial Group Theory》,《Virtual Knots. The State of the Art》 and 《Knot Theory》.  He held many international conferences, such as "4-th Russian China Russia-China on Knot theory and Related topics" and three International Conferences in the Mathematical Institute (Oberwolfach) on knot theory and low-dimensional topology".

 

Rota-Baxter operators, skew braces and Yang-Baxter equation

Speaker:Valeriy Bardakov

Time:2021.12.17 15:00--17:00 

Location:Zoom               

               Meeting ID: 862 062 0549

               Password: 2021

Meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

Abstract: 

Bio:Valeriy Bardakov is a professor of Sobolev Institute of Mathematics with holding a joint position at Laboratory of Topology and Dynamics of Novosibirsk State University. Valeriy Bardakov is a famous expert on braid theory, knot theory and group theory with over 90 publications in the area.

 

Variational Bihamiltonian Cohomology and Integrable Hierarchie

Speaker:Youjin Zhang(Tsinghua University)

Time:2021.12.10 10:00-12:00

Location:Meeting Tencent

                 Meeting ID:924-966-280

Meeting:https://meeting.tencent.com/dm/4PgMu2SMQi39

Abstract: In order to study deformations of Virasoro symmetries of the bihamiltonian integrable hierarchies associated to semisimple Frobenius manifolds, we introduce the notion of variational bihamiltonian cohomology, and compute the cohomology groups that will be used in our study of deformations of Virasoro symmetries. To illustrate its application, we classify the conformal bihamiltonian structures with semisimple hydrodynamic limits.

Bio:张友金,清华大学数学科学系教授,杰出青年基金获得者,教育部长江学者特聘教授。1994年于中国科技大学数学系获博士学位,1990-1991年在俄罗斯斯捷克洛夫数学所圣彼得堡分所作访问学者,1994-1999年在意大利国际理论物理中心、意大利国际高等研究院和日本京都大学数学系从事博士后研究,1999年起任清华大学数学科学系教授。主要从事数学物理与可积系统理论方面的研究,在双哈密顿可积方程簇的分类及其与Frobenius流形、Gromov-Witten不变量理论的联系等方面做出了重要的工作。在Invent. Math., CMP, Adv. Math.等顶尖杂志上发表学术论文50余篇。

 

O-operators on Lie infinity algebras

SpeakerJoana Nunes da Costa(University of Coimbra - Portugal)

Time:2021.12.03 16:00-18.00

Location:Zoom

              ID:862 062 0549

              Password:2021

ZOOM meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09  

Abstract: We define O-operators on a Lie infinity algebra E with respect to an action of E on another Lie infinity algebra. We characterize these operators as Maurer-Cartan elements of a certain Lie infinity algebra obtained by Voronov's higher derived brackets construction. We determine the Lie infinity algebra that controls the deformation of O-operators with respect to a fixed action.

Bio:Joana Nunes da Costa is a professor of University of Coimbra, Portugal. She mainly works on Poisson geometry and mathematical physics.

 

The Lang-Trotter Conjecture and the Hardy-Littlewood Conjecture

Speaker:Hourong Qin(Nanjing University)

Time:2021.11.26  09:00-11.00 

Location:Meeting Tencent

                 Meeting ID:662 784 567

Meeting:https://meeting.tencent.com/dm/qloVYRjPFHvl

Bio: 秦厚荣教授现任南京大学数学系系主任,江苏国家应用数学中心主任,中国数学会常务理事,中国科学-数学编委,江苏省数学学会第十届,十一届理事长,第十二届监事会主席。1999年获得国家杰出青年基金,2004年受聘教育部长江学者计划特聘教授,首批入选国家“百千万人才计划”(2004年),享受国务院特殊津贴。他的研究方向主要是代数数论和代数K理论。他在同余数这一历史悠久问题上的研究上取得了重要成果;在数域的Tame核、Tate核方面做出了原创性工作,引发了大量后续工作;解决了田野,Browkin等人的多个猜想;在著名的椭圆曲线Anomalous素数的Mazur猜想以及Lang-Trotter猜想的研究中取得了突破。他在J. Reine Angew Math., P. London Math. Soc., Math. Ann. 等国际著名刊物上发表了数十篇论文,研究结果在国际同行中产生了广泛而积极的影响,被国外同行称为“秦的方法”,多次在高水平国际学术会议上作大会邀请报告。

Quantum GIM of N-fold affinization and quantum toroidal algebra

 

Speaker:Yun Gao(York University)

Time:2021.11.19  09:00-11.00 

LocationZoom

                 Meeting ID:862 062 0549

                 Password:2021

ZOOM meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

Abstract: Generalized intersection matrix (GIM) Lie algebras were introduced by Slodowy in the study of elliptic singularity. GIM Lie algebras of N-fold affinization were studied by Berman-Moody, Benkart-Zelmanov and among others. In this talk we will talk about quantum GIM algebras of N-fold affinization and quantum toroidal algebras.

Bio: 郜云教授是加拿大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重要工作。他已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 American athematical Society 1997和2002)。

 

Embedding of Loday algebras into Rota-Baxter algebras

SpeakerVsevolod Gubarev(Sobolev Institute of Mathematics,Novosibirsk State University)

Time:2021.11.12 15:00-17:00 

LocationZoom

                 Meeting ID:862 062 0549

                 Password:2021

ZOOM meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

AbstractThe classical Poincare–Birkhoff–Witt states that every Lie algebra injectively embeds into its universal enveloping associative algebra and this enveloping algebra in some sense does not depend on the Lie product (PBW-property). It is known that every Rota–Baxter algebra of weight 0/1 gives rise to a prealgebra/postalgebra. In 2013, it was proved that every pre- or postalgebra injectively embeds into appropriate Rota–Baxter algebra of weight 0 or 1 respectively. We study the structure and the PBW-property of the universal enveloping Rota–Baxter algebra of a pre- and post-Lie algebra.

Bio:Vsevolod Gubarev ,Senior researcher in Sobolev Institute of Mathematics and senior teacher in Novosibirsk State University (both in Novosibirsk, Russia). Area of interest: ring theory.  

 

Rota-Baxter operators and non-skew-symmetric solutions of the classical Yang-Baxter equation on quadratic Lie algebras

SpeakerMaxim Goncharov (Sobolev Institute of Mathematics,Novosibirsk State University)

Time:2021.11.5 15:00-17:00 

LocationZoom

                 Meeting ID:862 062 0549

                 Password:2021

ZOOM meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

AbstractGiven a quadratic Lie algebra, it is well-known that skew-symmetric solutions of the classical Yang-Baxter equation are in one-to-one correspondence with skew-symmetric Rota-Baxter operators of weight zero. In this talk, we will study connections between Rota-Baxter operators of non-zero weight and non-skew-symmetric solutions of the classical Yang-Baxter equation on finite-dimensional quadratic Lie algebras. Particular attention will be given to the case of simple finite-dimensional Lie algebras.

Bio:Maxim Goncharov, Ph.D., Senior research fellow in Sobolev Institute of Mathematics, Associate Professor at Novosibirsk State University.

 

Revisiting and extending Poisson-Nijenhuis structures

 

SpeakerHenrique Bursztyn (Instituto Nacional de Matemática Pura e Aplicada)

Time:2021.10.22 08:00-09:00

Location:Zoom

                 Meeting ID:862 062 0549

                 Password:2021

ZOOM meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

AbstractPoisson-Nijenhuis structures arise in various contexts, such as the theory of integrable systems and Poisson-Lie theory. I will revisit this notion from a new perspective and show how it can be extended to the realm of Dirac structures. I also hope to mention applications to integration problems. The talk is based on joint work with T. Drummond and C. Netto.

Bio:Henrique Bursztyn is a professor of Instituto Nacional de Matemática Pura e Aplicada (IMPA), Brazil. His research interest includes Poisson geomety, Dirac structures, Lie groupoids, Lie algebroids, deformation quantization and mathematical physics. He published more than 70 papers in high level journals, such as Duke Math. J,  J. Reine Angew. Math.,  Compos. Math.,  Comm. Math. Phys.,  Int. Math. Res. Not. IMRN, Adv. Math.  

Renormalization of quasisymmetric functions

SpeakerLi Guo (Rutgers University-Newark)

Time:2021.10.15 09:00

Location:Zoom

                 Meeting ID:862 062 0549

                 Password:2021

ZOOM meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

 

AbstractThe Hopf algebra of quasisymmetric functions (QSym) has played a central role in algebraic combinatorics and has broad applications. A natural linear basis of QSym is the set of monomial quasisymmetric functions defined by compositions, that is, vectors of positive integers. Extending such a definition for weak compositions, that is, vectors of nonnegative integers, leads to divergent expressions. This difficulty was addressed by a formal regularization in a previous work with Jean-Yves Thibon and Houyi Yu. Here we apply the method of renormalization in the spirit of Connes and Kreimer and realize weak composition quasisymmetric functions as power series. The resulting Hopf algebra has the Hopf algebra of quasisymmetric functions as both a Hopf subalgebra and a Hopf quotient algebra. It also gives a realization of free commutative Rota-Baxter algebra on one generator by weak quasisymmetric functions and thus addresses a question raise by Rota many years ago. This is a joint work with Houyi Yu and Bin Zhang. 

Bio:  郭锂,美国罗格斯大学纽瓦克分校教授。郭锂博士于兰州大学获学士学位,于武汉大学获硕士学位,于华盛顿大学获博士学位,并在俄亥俄州立大学、普林斯顿高等研究院和佐治亚州大学作博士后。郭锂博士的数论工作为怀尔斯证明费马大定理的文章所引用,并将重整化这一物理方法应用于数学研究。他近年来推动Rota-Baxter代数及相关数学和数学物理的研究,应邀为美国数学会在“What Is”栏目中介绍Rota-Baxter代数,并出版这个领域的第一部专著。研究涉及结合代数,李代数,Hopf代数,operad,数论,组合,计算数学,量子场论和可积系统等广泛领域.

 

Title:Koszul duality: old and new

Speaker:Andrey Lazarev(University of Lancaster)

Time:2021.10.8 15:00

Location:Zoom

                 Meeting ID:862 062 0549

                 Password:2021

ZOOM meeting:https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

 

AbstractKoszul duality is a phenomenon occurring in homological algebra and neighbouring fields, such as rational homotopy theory, representation theory, algebraic geometry, operads and operadic algebras. In this talk I will outline a modern approach to deformation theory based on Koszul duality and explain how it can be globalized.  

 

Bio:Andrey Lazarev is a professor of pure mathematics in the University of Lancaster. His recent research deals with homotopy theory of differential graded algebras and categories, derived categories and higher phenomena. It has applications in rational homotopy theory, theory of operads and operadic algebras, algebraic topology and pure algebra. Andrey Lazarev is the Managing Editor of the journal《Bulletin of the London Mathematical Society》,as well as a Member of the Editorial Board of  the journal《Higher_Structures》.

 

 

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