Geometric aspects of the ground state of magnetic Laplacians on domains of the plane
Analysis and Geometry Seminar
21st June 2023, 3:00 pm – 4:00 pm
Fry Building, 2.41
I will survey a few classical and recent results for the ground state (that is the first eigenvalue of the spectrum) of magnetic Laplacians on domains of the plane. I will consider the Aharonov-Bohm magnetic Laplacian (curvature zero) and the magnetic Laplacian with constant curvature. I will discuss isoperimetric inequalities and geometric bounds. I will not describe the different proofs, but I will take the time to mention different open questions.
The recent results are obtained in different papers in collaboration with Corentin Lena, Luigi Provenzano, Alessandro Savo.
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