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Conferencias impartidas por Alessandro Savo

Spectrum and involutions

Università di Roma

This is a joint work with Bruno Colbois. Consider a compact Riemannian manifold MM with an involutive isometry γ\gamma, and assume that the distance of any point to its image under γ\gamma is bounded below by a positive constant β\beta (the smallest displacement). We observe that this simple geometric situation has a strong consequences on the spectrum of a large class of γ\gamma-invariant operators DD (including the Schrödinger operator acting on functions and the Hodge Laplacian acting on forms): roughly speaking, the gap λ2(D)λ1(D)\lambda_2(D)-\lambda_1(D) between the first and the second eigenvalue of DD is uniformly bounded above by a constant depending only on the displacement β\beta (in particular, not depending on DD).

The fundamental tones of a convex body

Università di Roma

M-23

Alessandro Savo

Università di Roma (Italia)

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This activity is supported by the research projects EUR2024.153556, PID2023-150727NB-I00, , PID2023-151060NB-I00, PID2022-142559NB-I00, CNS2022-135390 CONSOLIDACION2022, PID2020-118137GB-I00, PID2020-117868GB-I00, PID2020-116126GB-I00.