Title:Dirac Operators in Riemannian Geometry
Speaker:Yongqiang Tian（Central South University）
Time:Monday, October 17, 2022, 14:00-15:00
Location: B201-1, Mingde Building
Abstract：As is well known, the Dirac operator plays a crucial role in Alain Connes’ noncommutative geometry. In this talk, we will revisit the construction of Dirac operatorson Riemannian spin manifolds. Some basic knowledge of classical geometry is required.
Working on a spectral triple (A,H,D), i.e. the noncommutative generalization of aRiemannian spin manifold, places you into the operator framework. So, in order toget some non-trivial results on it, both summability and regularity concerning theabstract Dirac operator D (self-adjoint, possibly unbounded) are usually assumedto be good enough. However, life is not smooth, especially when your algebra A isnot ‘smooth’ either. Suppose now we have a nice algebra acting on Hilbert spaceH, then how to construct a proper Dirac operator D to guarantee the summabilityand regularity? There is no routine method in the noncommutative setting. Thismotivates us to look for some inspirations from the starting point: Riemanniangeometry! And we will provide a few examples.
More information:Graduate Student Seminar
