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Seminar Spectral Geometry
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Title: Spectral shift via lateral variation

Abstract:聽Our study is motivated by earlier results about nodal count of Laplacian eigenfunctions on manifolds and graphs that share the same flavor: the nodal count鈥檚 鈥漝eviation鈥� is equal to the Morse index of a certain 鈥漞nergy functional鈥� . In the hindsight, in all these results, the nodal count can be understood as the spectral shift resulting from perturbing the operator in an appropriate way. This brings us to the following general result (joint with G. Berkolaiko): the spectral shift can be recovered as the stability (Morse) index of the eigenvalue with respect to small 鈥漧ateral鈥� variations of the perturbation.