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題目一：  Ternary Grassmann algebras and Fock spaces with a view to hypersymmetry

摘要: Supersymmetry is based on Z2-graded algebras, of which Clifford and Grassmann algebras are classical examples as they allows us to consider a Fock space of monogenic function and build most of the necessary ingredients for a theory of entire functions. But more general settings (for example, quarks) require a more general type of supersymmetry. In this talk we shall present the groundwork for an Ito;/Malliavin stochastic calculus and a Hida’s white noise analysis in the context of a supersymmetry based on Z3-graded algebras. To this end, we establish a ternary Fock space and the corresponding strong algebra of stochastic distributions and present its application in the study of stochastic processes.

題目二：Pseudo-differential Operator Calculus in Discrete Clifford Analysis

摘要: In this talk we present discrete pseudo-differential operators in the context of Clifford analysis. We will

establish the necessary calculus which will be used to discuss questions like boundedness and compactness

of operators. In the end, we will discuss well-known examples from Clifford analysis as well as give new

examples including discrete Dirac operators with non-constant coefficients.

Paula Cerejeiras教授簡介：現(xiàn)任職于葡萄牙Aveiro大學(xué)數(shù)學(xué)系，副教授。1992-1997于葡萄牙Aveiro大學(xué)和比利時Ghent大學(xué)攻讀博士學(xué)位，獲得博士學(xué)位。主要研究領(lǐng)域為現(xiàn)代分析（克里福德分析，調(diào)和分析，邊值問題）及其應(yīng)用，發(fā)表論文70多篇，培養(yǎng)了一大批博士研究生。她主持申請國家基金，并邀請大量中國學(xué)者去Aveiro大學(xué)從事短期和長期數(shù)學(xué)研究。組織過多次國際學(xué)術(shù)會議。是ISSAC協(xié)會創(chuàng)始成員。下列雜志的編委：AACA(Advances in Applied Clifford Algebras) (Springer)、IJWMIP(International Journal of Wavelets, Multiresolution and Information Processing)、CAOT (Complex Analysis and Operator Theory) (Springer)。