應(yīng)yl7703永利官網(wǎng)邀請(qǐng)，江西師范大學(xué)鄭上華副教授，南京信息工程大學(xué)張毅博士將于2022年3月12日舉辦線上學(xué)術(shù)講座，歡迎廣大師生參加。

報(bào)告題目：Interlacing and integrals of Hurwitz series and differential equations

時(shí)間：3月12日下午14:30

騰訊會(huì)議ID：368 560 569

報(bào)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 $\exp$.

報(bào)告人簡(jiǎn)介：鄭上華，博士,江西師范大學(xué)副教授，碩士生導(dǎo)師。于2015年6月畢業(yè)于蘭州大學(xué)，獲得理學(xué)博士學(xué)位。主要從事羅巴代數(shù)，項(xiàng)重寫系統(tǒng)和Gr?bner-Shirshov基理論等領(lǐng)域的研究。主持國(guó)家自然科學(xué)基金2項(xiàng)和江西省教育廳科技項(xiàng)目1項(xiàng)。在中國(guó)科學(xué)、J. Lie Theory、Comm. Algebra、Pacific J. Math.等期刊發(fā)表學(xué)術(shù)論文數(shù)篇。

報(bào)告題目：The Cohomology of relative cocycle weighted Reynolds operators and NS-pre-Lie algebras

時(shí)間：3月12日下午15:30

騰訊會(huì)議ID：368 560 569

報(bào)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.

報(bào)告人簡(jiǎn)介：張毅，博士，南京信息工程大學(xué)講師。于2020年8月畢業(yè)于yl7703永利官網(wǎng)，獲理學(xué)博士學(xué)位。2019年8月--2020年8月受國(guó)家留學(xué)基金委(CSC)資助，在美國(guó)南加州大學(xué)數(shù)學(xué)系聯(lián)合培養(yǎng)，研究領(lǐng)域是代數(shù)表示理論，Rota-Baxter代數(shù)與Hopf代數(shù)。目前以第一作者或通訊作者身份在J. Algebra，Pacific J. Math.，J. Algebraic Combin.，Comm. Algebra，中國(guó)數(shù)學(xué)進(jìn)展，中國(guó)數(shù)學(xué)年刊等國(guó)內(nèi)外行業(yè)主流雜志發(fā)表論文十余篇。現(xiàn)主持國(guó)家自然基金青年基金一項(xiàng)，參與國(guó)家自然基金面上項(xiàng)目?jī)身?xiàng)。