学术报告
A spectral flow formula through Brouwer degree for semi-Riemannian geodesics
题目：A spectral flow formula through Brouwer degree for semi-Riemannian geodesics
报告人： Alessandro Portaluri 教授 （意大利都灵大学）
摘要: Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in the presence of a potential. Our purpose in this talk is to show how to extend to perturbed geodesics on semi-Riemannian manifolds the well known Morse Index Theorem. When the metric is indefinite, the Morse index of the energy functional becomes infinite and hence, in order to obtain a meaningful statement, we substitute the Morse index by its relative form, given by the spectral flow of an associated family of index forms. We also introduce a new counting for conjugate points, which need not to be isolated in this context, and prove that our generalized Morse index equals the total number of conjugate points. Finally we study the relation with the Maslov index of the flow induced on the Lagrangian Grassmannian.
At the end of the talk some open problems and new research directions will be discussed.
时间：3月21日（周一）上午10:30-11:30
地点：首都师大北一区文科楼210教室
欢迎全体师生积极参加！
