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华南农业大学数信学院系列讲座
报告人：Paula Cerejeiras教授(阿威罗大学)
题目一： Ternary Grassmann algebras and Fock spaces with a view to hypersymmetry
日期：2024年7月16日
时间：9:30-11:00(北京时间)
地点：数学与信息学院西楼605
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.
题目二：Pseudo-differential Operator Calculus in Discrete Clifford Analysis
日期：2024年7月16日
时间：11:00-12:30(北京时间)
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教授简介：现任职于葡萄牙Aveiro大学数学系，副教授。1992-1997于葡萄牙Aveiro大学和比利时Ghent大学攻读博士学位，获得博士学位。主要研究领域为现代分析（克里福德分析，调和分析，边值问题）及其应用，发表论文70多篇，培养了一大批博士研究生。她主持申请国家基金，并邀请大量中国学者去Aveiro大学从事短期和长期数学研究。组织过多次国际学术会议。是ISSAC协会创始成员。下列杂志的编委：AACA(Advances in Applied Clifford Algebras) (Springer)、IJWMIP(International Journal of Wavelets, Multiresolution and Information Processing)、CAOT (Complex Analysis and Operator Theory) (Springer)。