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Sino-Russian Mathematics Center-JLU Colloquium (2021.11.26)

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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