中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

 

报告人:王好武 博士(Institute for Basic Science, Center for Geometry and Physics, Korea
  目:Rings of Jacobi forms of lattice index
  间:2022.05.16(星期一),15:00-17:00
  点:腾讯会议:819-257-218
  要:In 1985 Eichler and Zagier defined the Jacobi form as a common generalization of theta functions, modular forms, and elliptic functions. Given an even positive-definitte lattice, the associated Jacobi forms form a graded ring. It is an open problem whether this ring is finitely generated. In this talk we will first briefly introduce the theory of Jacobi forms, and then discuss the ring structure of Jacobi forms associated with irreducible root systems, rank-two lattices and the Leech lattice.
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报告人:王好武 博士(Institute for Basic Science, Center for Geometry and Physics, Korea
  目:Free algebras of modular forms
  间:2022.05.18(星期三),15:00-17:00
  点:腾讯会议:468-680-024
  要:It is an interesting problem in the theory of modular forms to determine the structure of rings of modular forms, that is, to find explicit generators and their relations. In this talk, we will introduce the modular Jacobian approach to construct and classify the arithmetic groups acting on symmetric domains of type IV attached to O(n,2) or complex balls attached to U(n,1), for which the rings of modular forms are freely generated.

 

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