应数学与统计学院邀请，江西师范大学郑上华副教授，南京信息工程大学张毅博士将于2022年3月12日举办线上学术讲座，欢迎广大师生参加。

报告题目：Interlacing and integrals of Hurwitz series and differential equations

时间：3月12日下午14:30

腾讯会议ID：368 560 569

报告摘要：In this talk, we first introduce the unlacing of Hurwitz series, which can be viewed as an inverse of interlacing, and develop the basic properties of unlacing, interlacing and integral of Hurwitz series. We then show that multiplication of interlacing of Hurwitz series by basis elements can be also rewritten as an interlacing, and provide the explicit multiplication formula in terms of Hadamard products. Finally, we investigate the natural exponential function $\exp$, and realize the method of reduction of order in the ring of Hurwitz series by using $\exp$.

报告人简介：郑上华，博士,江西师范大学副教授，硕士生导师。于2015年6月毕业于兰州大学，获得理学博士学位。主要从事罗巴代数，项重写系统和Gröbner-Shirshov基理论等领域的研究。主持国家自然科学基金2项和江西省教育厅科技项目1项。在中国科学、J. Lie Theory、Comm. Algebra、Pacific J. Math.等期刊发表学术论文数篇。

报告题目：The Cohomology of relative cocycle weighted Reynolds operators and NS-pre-Lie algebras

时间：3月12日下午15:30

腾讯会议ID：368 560 569

报告摘要：Unifying various generalizations of the important notions of Reynolds operators, the relative cocycle weighted Reynolds operators are studied. Here cocycle weighted means the weight of the operators is given by a 2-cocycle rather than by a scaler as in the classical case. We show that the operators and 2-cocycles uniquely determine each other. We further give a characterization of relative cocycle weighted Reynolds operators in the context of pre-Lie algebras. We construct an explicit graded Lie algebra whose Maurer-Cartan elements are given by a relative cocycle weighted Reynolds operator, which makes it possible to construct a cohomology for the relative cocycle weighted Reynolds operator. This cohomology can also be seen as the cohomology of a certain pre-Lie algebra with coefficients in a suitable representation. Then we consider formal deformations of relative cocycle weighted Reynolds operators in the view of cohomology. Finally, we introduce the notation of NS-pre-Lie algebras and show NS-pre-Lie algebras naturally induce pre-Lie algebras and L-dendriform algebras.

报告人简介：张毅，博士，南京信息工程大学讲师。于2020年8月毕业于兰州大学数学与统计学院，获理学博士学位。2019年8月--2020年8月受国家留学基金委(CSC)资助，在美国南加州大学数学系联合培养，研究领域是代数表示理论，Rota-Baxter代数与Hopf代数。目前以第一作者或通讯作者身份在J. Algebra，Pacific J. Math.，J. Algebraic Combin.，Comm. Algebra，中国数学进展，中国数学年刊等国内外行业主流杂志发表论文十余篇。现主持国家自然基金青年基金一项，参与国家自然基金面上项目两项。