Geometric Structures seminar - Igor Zelenko - June 16, 2022 - 2:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Speaker: Igor Zelenko, Texas A&M University

Title: Morse inequalities for eigenvalue branches of generic families of self-adjoint matrices

Time: June 16, 2022, 2:00 pm (Rome Time)
Venue: room 134* (*to be confirmed)
on zoom at this link:
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

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Abstract:
The eigenvalue branches of families of self-adjoint matrices are not smooth at points corresponding to repeated eigenvalues (called diabolic points or Dirac points). Generalizing the notion of critical points as points for which the homotopical type of (local) sub-level set changes after the passage through the corresponding value, in the case of the generic family we give an effective criterion for a diabolic point to be critical for those branches and compute the contribution of each such critical point to the Morse polynomial of each branch, getting the appropriate Morse inequalities as a byproduct of the theory. These contributions are expressed in terms of the homologies of Grassmannians. The motivation comes from the Floquet-Bloch theory of Schroedinger equations with periodic potential and other problems in Mathematical Physics. The talk is based on the joint work with Gregory Berkolaiko.

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Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/