报告题目：Erlangen Program: transformation groups and geometries
时 间：2026年11月21日 (星期六) 09：30
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和研究生
报告摘要：In 1872, as being appointed to a chair at the University of Erlangen, Felix Klein delivered an inaugural address proposing a new unifying principle for classifying the various geometries. This address is known as the Erlangen Program. According to Erlangen Program, a geometry is a set S, called a space, on which a group G operates. The study of properties invariant under the operations of G is called a geometry.In this talk, we will first revisit the traditional high school geometries such as Euclidean geometry from the Klein’s viewpoint. We will use the transformation groups of isometries, similarities and collineations to study the various geometries of Euclidean, similarity and affine types, respectively. As a model of non-Euclidean geometry, we will then talk about projective space on which a projective linear group operates. By viewing the above-mentioned groups as subgroups of the projective linear group, the traditional geometries may be classified as certain sub-geometries of the projective geometry with various invariants.
报告人简介：杜杰，澳大利亚新南威尔士大学教授，博士生导师。1982年1月苏州大学本科毕业, 1987年7月华东师范大学博士毕业。在Weyl群的胞腔分解、代数群，q-Schur代数、Ringel-Hall 代数及量子群和量子超群等方面取得了一系列原创性的成果。 相关成果发表在Adv. Math., Comm. Math. Phys., Int. Math. Res. Not., J. Reine Angew. Math., Math. Z., Proc. London Math. Soc., Sci. China Math., Trans. Amer. Math. Soc.等国际著名数学学术杂志上100余篇。与合作者编著专著2本，分别由美国数学会和伦敦数学会发表。 曾担任多个数学类学术杂志编委。作为项目负责人多次获得澳大利亚基金委的资助。