报　告　题　目　及　摘　要

报告人：白承铭（南开大学）
报告题目: Classification of left-symmetric algebraic structures on Witt and Virasoro algebras
报告摘要: We introduce some classification results on the left-symmetric algebraic structures on Witt and Virasoro algebras including the graded cases, the super cases and the non-graded cases.

报告人：丁祥茂（中国研究院数学与系统研究院）
报告题目: Parafermion, TBA and Cluster Algebras
报告摘要: TBA

报告人：郭锂（Rutgers大学，兰州大学）
报告题目: Rota-Baxter Operators on Associative Algebras, Lie Algebras and Generalizations
报告摘要: A Rota-Baxter operator was first defined on an associative algebra from probability and combinatorics studies in the 1960s. Then in special cases it was also found in Lie algebra in the 1980s as the operator form of the classical Yang-Baxter equation. Recently, the efforts to understand the relationship between the Rota-Baxter operator in these two areas have led to the generalizations of this operator in both cases, as well as of classical and associative Yang-Baxter equations. We will report these developments in this talk. This is joint work with Chengming Bai and Xiang Ni.

报告人：胡乃红（华东师范大学）
报告题目: Loewy Filtration and Quantum de Rham Cohomology over Quantum Divided Power Algebras
报告摘要: In this talk, I'll talk about some results on the indecomposible modules for the Lusztig small quantum groups of type A. This is a joint work with H. Gu.

报告人：黄劲松（香港科技大学、山东大学）
报告题目: Dirac Cohomology and Dirac Induction
报告摘要: Let $G$ be a connected semisimple Lie group with a maximal compact group $K$ of equal rank. We use the Dirac cohomology of the unitary representations to define Dirac-induction from a representation of $K$ to the discrete series of $G$. This is closely related to the Dirac induction for the reduced group $C^*$-algebras $C^*_{red}(G)$ and a geometric construction of discrete series for semisimple Lie groups. Furthermore, we use Dirac cohomology of the Kostant's cubic Dirac operator to define Dirac-induction for compact Lie groups. This induction for compact Lie groups is simpler than the Bott's induction and is easier for calculation.

报告人：景乃桓（美国北卡罗纳州立大学，华南理工大学）
报告题目: Irreducible characters of spin wreath products
报告摘要: Exactly 100 years ago Schur constructed irreducible characters of the spin groups of the symmetric group and introduced the famous Schur Q-functions. Using ideas from affine Lie algebras and McKay correspondence, Frenkel, Jing and Wang fixed the irreducible characters for the spin group of the wreath products for the symmetric group without knowing the complete character table. In this work we will generalize Schur's work and completely determine all character values for the spin wreath products in type A case.

报告人：李方（浙江大学）
报告题目: Graded Hochschild cohomology and its graded Lie structure on path algebras
报告摘要: TBA

报告人：刘文德（哈尔滨师范大学）
报告题目：The minimal number of the generators for simple Lie superalgebras
摘要：In this talk we state a recent result: Over an algebraically closed field of characteristic zero, any finite-dimensional simple Lie superalgebra is generated by ONE element (equivalently, by two homogeneous elements).

报告人：孟国武（香港科技大学）
报告题目: Euclidean Jordan Algebras and the Universal Kepler Problem
报告摘要: For each simple euclidean Jordan algebra, the analogues of Hamiltonian, angular momentum and Lenz vector in the Kepler problem are introduced. The analogue of the hidden symmetry algebra generated by Hamiltonian, angular momentum and Lenz vector is also derived. Finally, we sketch how to arrive at a general theory for which both the Kepler problem and the oscillator problem are special examples.

报告人：芮和兵（华东师范大学）
报告题目: The quantized walled Brauer algebra
报告摘要: I will talk about some results on the representations of the quantized walled Brauer algebras. This is a joint work with Lingliang Song.

报告人：谭绍滨（厦门大学）
报告题目: Integral Irreducible Representations for Extended Affine Lie Algebras of Type A
报告摘要: In this talk we are going to deal with the explicit realizations of integral irreducible representations for extended affine Lie algebras coordinated by quantum torus or Jordan torus. The work is coauthored with Dr. Xuewu Chang and Dr. Fulin Chen.

报告人：吴泉水（复旦大学）
报告题目: Twisted Calabi-Yau algebras and AS-regular Algebras
报告摘要: I will talk about the relations between the twisted (graded) Calabi-Yau algebras and AS-regular Hopf (connected graded) Algebras. Some recent research on this topic will be reported.

报告人：惠昌常 （北京师范大学）
报告题目: Homological ring epimorphisms and universal pairs
报告摘要: Homological ring epimorphisms are often used in algebraic K-theory and modern representation theory. When a universal localization is homological seems to be an interesting question. In this talk, we give a new characterization for a universal localization related to a 'universal' pair of ring homomorphisms to be homological. This gives rise to a variety of new recollements of derived module categories. For example, if $\lambda: R\rightarrow S$ is an injective homological ring epimorphism between commutative rings $R$ and $S$ then the derived category of the endomorphism ring of the $R$-module $S \oplus S/R$ always admits a recollement of the derived module categories of $R$ and $S\otimes_R {\rm End}_R(S/R)$. This reports a part of a joint work with H.X.Chen.

报告人：徐晓平（中国研究院数学与系统研究院）
报告题目: A New Functor from D5-Mod to E6-Mod
报告摘要: It is well known that the minimal dimension of irreducible modules over the simple Lie algebra of type E6 is 27. We find a first-order differential operator repre-sentation of the Lie algebra on the polynomial algebra in 16 independent variables, whose corresponding Lie group representation is given by fractional transformations on 16-dimensional space. Using this representation and Shen's idea of mixed product, we construct a functor from D5-Mod to E6-Mod, where a hidden central transformation is involved. A condition for the functor to map a finite-dimensional irreducible D5-module to an infinite-dimensional irreducible E6-module in terms of the constant value taken by the central transformation is obtained. The result could be useful in understanding the quantum field theory with E6 symmetry and symmetry analysis of partial differential equations.

报告人：杨文力（西北大学）
报告题目: Superalgebra $D(2,1;\alpha)$ and associated current algebra
报告摘要: The free-field representations of the $D(2,1;\alpha)$ current superalgebra and the corresponding energy-momentum tensor are constructed. The related screening currents of the first kind are also presented.

报告人：张贺春（清华大学）
报告题目: Invariant theory and eqivariant quantization
报告摘要: I will talk about the deformation of some symmetric algebra. The deformed algebras are subalgebras of quantized enveloping algebras of Kac-Moody algebras.