Poisson几何、李理论与数学物理研讨会

  

时间11月19日	报告人	报告题目
8:30-9:10	陈良云	Super-biderivations, triple derivations and triple homomorphisms on Lie superalgebras
9:15-9:55	李宁	Local theta correspondence and invariants attached certain representations
10:10-10:50	徐森荣	Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras
10:55-11:35	李彦鹏	Poisson-Lie groups and cluster algebras: an introduction
13:20-14:00	徐晓濛	Integrable systems on Lie-Poisson spaces
14:05-14:45	郎红蕾	Classification of multiplicative multivector fields on a Lie groupoid
15:00-15:40	刘杰锋	Lie n-algebras and cohomologies of relative Rota-Baxter operators on n-LieRep pairs
15:45-16:25	张涛	On Hom-Lie antialgebras
时间20日	报告人	报告题目
8:30-9:10	张斌	锥zeta值和双剖分关系
9:20-11:20	刘张炬	经典力学与量子力学的可观测量代数
13:00-13:40	郑驻军	量子信息简介、技术前沿以及相关数学问题
13:45-14:25	洪伟	Poisson structure, polyvector vector fields and toric varieties
14:40-15:20	裴俊	Splitting of Operads and Rota-Baxter Operators
15:25-16:05	于世卓	On the Kazhdan-Lusztig Maps and Some Poisson Homogeneous Spaces

题目：经典力学与量子力学的可观测量代数

报告人：刘张炬（北京大学）

摘要： 经典可观测量是状态空间(辛流形)上的函数，量子可观测量是波函数空间(希尔伯特空间)上的自伴算子。在这个报告中，我们介绍经典和量子可观测量代数的数学结构以及两者之间的关系。

题目：量子信息简介、技术前沿以及相关数学问题

报告人：郑驻军（华南理工大学）

摘要：该报告是从数学角度讲述量子信息。我们将从最基本的量子力学开始，介绍量子信息的一些基本内容、最新技术进展，最后给出量子信息中的一些数学问题。

题目：锥zeta值和双剖分关系

报告人：张斌（四川大学）

摘要：在这个报告里我们引入多元zeta值和双洗牌关系的推广：锥zeta值和双洗牌关系，从一个新的角度来理解多元zeta值的关系。这是基于锥和分式的有趣的对应关系。本报告是和郭锂，Sylvie Paycha 合作的结果。

题目：Super-biderivations, triple derivations and triple homomorphisms on Lie superalgebras

报告人：陈良云（东北师范大学）

摘要： In this talk, we  mainly introduce super-biderivations，triple derivations and  triple homomorphisms on Lie superalgebras.  We first prove that all super-biderivations on Lie superalgebras of Cartan type over the complex field are inner super-biderivations by their roots. Utilizing the weight space decomposition, we prove all skew-symmetric super-biderivations on the generalized Witt modular Lie superalgebra and contact Lie superalgebra are also inner super-biderivations. We described the intrinsic connections super-biderivations and centroids for Lie superalgebras. Moreover, every triple derivation of perfect Lie superalgebras with zerocenter is a derivation, and every triple derivation of their derivation algebras is an inner derivation. We prove that, under certain assumptions, homomorphisms, anti-homomorphisms, and sums of homomorphisms and anti-homomorphisms on Lie superalgebras are all triple homomorphisms.

题目：Integrable systems on Lie-Poisson spaces

报告人：徐晓濛（北京大学）

摘要：This talk will give an introduction to various known integrable systems on the dual of simple Lie algebras and discuss some unsolved problems. In particular, it will discuss a possible way to derive Gelfand-Zeitlin systems of symplectic Lie algebras, via Moser's trick and the theory of Stokes phenomenon.

题目：Classification of multiplicative multivector fields on a Lie groupoid

报告人：郎红蕾（中国农业大学）

摘要：The quotient of multiplicative multivector fields by the exact ones is a Morita invariant of a Lie groupoid. We use the first cohomology of its jet groupoid to give a classification of this quotient space. Infinitesimally, the differentials on the Lie algebroid are also classified. This is a joint work with Zhuo Chen.

题目：On Hom-Lie antialgebras

报告人：张涛（河南师范大学）

摘要： In this talk, we will introduce the notion of Hom-Lie antialgebras and crossed modules for Hom-Lie antialgebras. The representations and cohomology theory of Hom-Lie antialgebras are investigated. We prove that the equivalent classes of abelian extensions of Hom-Lie antialgebras are in one-to-one correspondence to elements of the second cohomology group. The notion of Nijenhuis operators of Hom-Lie antialgebra is introduced to describe trivial deformations. It is proved that the category of crossed modules for Hom-Lie antialgebras and the category of Cat1-Hom-Lie antialgebras are equivalent to each other. The relationship between the crossed module extension of Hom-Lie antialgebras and the third cohomology group are investigated. This is a joint work with Heyu Zhang, based on two papers: "On Hom-Lie antialgebra, Communications in Algebra, 48:8, 3204-3221" and "Crossed modules for Hom-Lie antialgebras, arxiv.1903.08870".

题目：Lie n-algebras and cohomologies of relative Rota-Baxter operators on n-LieRep pairs

报告人：刘杰锋（东北师范大学）

摘要：Based on the dg Lie algebra controlling deformations of ann-Lie algebra with a representation (called an n-LieRep pair), we construct a Lie n-algebra, whose Maurer-Cartan elements characterize relative Rota-Baxter operators on n-LieRep pairs.  The notion of an n-pre-Lie algebra is introduced, which is an algebraic structure behind the relative Rota-Baxter operators.  We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extensions of order m-deformations to order (m+1)-deformations of relative Rota-Baxter operators through the cohomology groups of relative Rota-Baxter operators. Moreover, we build the relation between the cohomology groups of relative Rota-Baxter operators on n-LieRep pairs and those on (n+1)-LieRep pairs by certain linear functions.

题目：Splitting of Operads and Rota-Baxter Operators

报告人：裴俊（西南大学）

摘要：We consider a procedure that splits the operations in any algebraic operad, generalizing previous notion of the successors for binary operads. The concept of a Rota-Baxter operator is defined for all operads. The well-known connection from Rota-Baxter operators to dendriform algebras and its numerous extensions are expanded as the link from (relative) Rota-Baxter operators on operads to splittings of the operads.

题目：Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras

报告人：徐森荣（江苏大学）

摘要：In this talk, we will introduce the notion of quasi-trace functions on Lie algebras. We will use linear functions, especially quasi-trace functions, to realize 3-dimensional 3-Lie algebras via each isoclass of 3-dimensional Lie algebras. We will classify all 4-dimensional 3-Lie algebras induced by quasi-trace functions. We will give two sufficient and necessary conditions on homomorphisms of Leibniz algebras and associative algebras for linear functions to be quasi-trace functions, from which we will construct representation of 3-Lie algebras induced by quasi-trace functions. We will also obtain some results on comparison of cohomologies via quasi-trace functions. This is a joint work in progress with Youjun Tan.

题目：Local theta correspondence and invariants attached certain representations

报告人：李宁（北京大学）

摘要：Roger Howe introduced the theory of local theta correspondence to relate the representation theory of pairs of reductive groups. These pairs are the so called reductive dual pairs. Moreover, local theta correspondence is a powerful tool in studying invariants attached to admissible representations. In this talk, I will give an example how local theta correspondence can be used in studying two geometric invariants: associated cycles and wave front cycles. In addition, I will briefly talk about the relationship between these two invariants and the space of generalized Whittaker models for certain representations of symplectic groups.

题目：Poisson-Lie groups and cluster algebras: an introduction

报告人：李彦鹏（日内瓦大学）

摘要：In this talk, I will give a brief introduction to the theory of Poisson-Lie groups and cluster algebras arising from Lie theory, together with their interplays.

题目：Poisson structure, polyvector vector fields and toric varieties

报告人：洪伟（武汉大学）

摘要：In this talk, we give a report on my work of holomorphic polyvector fields on toric varities and Poisson cohomology. And we give two open questions related to my work.

题目： On the Kazhdan-Lusztig Maps and Some Poisson Homogeneous Spaces

报告人：于世卓（南开大学）

摘要：In this talk, we first introduce Kazhdan-Lusztig maps and its Poisson geometric interpretations. Then, we use these maps to study some Poisson homogeneous spaces of the standard Poisson Lie group and a class of Poisson algebras associated to them. This is a joint work with Lu Jiang-Hua.