Title：Fredholm Conditions on Singular Spaces 

Speaker：乔  雨 （陕西师范大学）

Time：2017年12月8日    下午14:00--15:30

Room：东区管理科研楼   数学科学学院1418室

 

Abstract： In the 1980's, Alain Connes initiated his program of noncommutative differential geometry, especially the study of ``bad" spaces. It turns out that Lie groupoids are an effective tool to model many analysis and index problems on singular spaces. In this talk, we first recall the notion of manifolds with corners (following the work of Melrose). Then, we review the construction of group $C^*$-algebras via the representation theory of groups, the notion of Lie groupoids, and the construction of groupoid $C^*$-algebras via the representation theory of $C^*$-algebras. Next, we present the concept of a Fredholm groupoid, which is a class of groupoids for which certain characterization of Fredholm operators is valid, and then adopt $b$-calculus, scattering calculus, and edge calculus in the frame work of Fredholm groupoids. Finally, we discuss briefly the relation between Fredholm groupoids and index theory. This is joint work with Catarina Carvalho and Victor Nistor.