時間11月19日 |
報告人 |
報告題目 |
8:30-9:10 |
陳良雲 |
Super-biderivations, triple derivations and triple homomorphisms on Lie superalgebras |
9:15-9:55 |
李甯 |
Local theta correspondence and invariants attached certain representations |
10:10-10:50 |
徐森榮 |
Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras |
10:55-11:35 |
李彥鵬 |
Poisson-Lie groups and cluster algebras: an introduction |
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|
|
13:20-14:00 |
徐曉濛 |
Integrable systems on Lie-Poisson spaces |
14:05-14:45 |
郎紅蕾 |
Classification of multiplicative multivector fields on a Lie groupoid |
15:00-15:40 |
劉傑鋒 |
Lie n-algebras and cohomologies of relative Rota-Baxter operators on n-LieRep pairs |
15:45-16:25 |
張濤 |
On Hom-Lie antialgebras |
時間20日 |
報告人 |
報告題目 |
8:30-9:10 |
張斌 |
錐zeta值和雙剖分關系 |
9:20-11:20 |
劉張炬 |
經典力學與量子力學的可觀測量代數 |
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|
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13:00-13:40 |
鄭駐軍 |
量子信息簡介、技術前沿以及相關數學問題 |
13:45-14:25 |
洪偉 |
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 |
題目：經典力學與量子力學的可觀測量代數
報告人：劉張炬（北京大學）
摘要： 經典可觀測量是狀态空間(辛流形)上的函數，量子可觀測量是波函數空間(希爾伯特空間)上的自伴算子。在這個報告中，我們介紹經典和量子可觀測量代數的數學結構以及兩者之間的關系。
題目：量子信息簡介、技術前沿以及相關數學問題
報告人：鄭駐軍（華南理工大學）
摘要：該報告是從數學角度講述量子信息。我們将從最基本的量子力學開始，介紹量子信息的一些基本内容、最新技術進展，最後給出量子信息中的一些數學問題。
題目：錐zeta值和雙剖分關系
報告人：張斌（四川大學）
摘要：在這個報告裡我們引入多元zeta值和雙洗牌關系的推廣：錐zeta值和雙洗牌關系，從一個新的角度來理解多元zeta值的關系。這是基于錐和分式的有趣的對應關系。本報告是和郭锂，Sylvie Paycha 合作的結果。
題目：Super-biderivations, triple derivations and triple homomorphisms on Lie superalgebras
報告人：陳良雲（東北師範大學）
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.
題目：Integrable systems on Lie-Poisson spaces
報告人：徐曉濛（北京大學）
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.
題目：Classification of multiplicative multivector fields on a Lie groupoid
報告人：郎紅蕾（中國農業大學）
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.
題目：On Hom-Lie antialgebras
報告人：張濤（河南師範大學）
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".
題目：Lie n-algebras and cohomologies of relative Rota-Baxter operators on n-LieRep pairs
報告人：劉傑鋒（東北師範大學）
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.
題目：Splitting of Operads and Rota-Baxter Operators
報告人：裴俊（西南大學）
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.
題目：Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras
報告人：徐森榮（江蘇大學）
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.
題目：Local theta correspondence and invariants attached certain representations
報告人：李甯（北京大學）
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.
題目：Poisson-Lie groups and cluster algebras: an introduction
報告人：李彥鵬（日内瓦大學）
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.
題目：Poisson structure, polyvector vector fields and toric varieties
報告人：洪偉（武漢大學）
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.
題目： On the Kazhdan-Lusztig Maps and Some Poisson Homogeneous Spaces
報告人：于世卓（南開大學）
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.
