题目：Dirac Operators in Riemannian Geometry
报告人：田永强（中南大学）
时间：2022年10月17日（星期一），14:00-15:00
地点：哈工大明德楼B区201报告厅
摘要：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.
更多信息：研究生研讨班
