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SUMMARY:Eigenvalue inequalities for the magnetic Laplacian - Corentin Lén
 a (University of Padua)
DTSTART:20260401T100000Z
DTEND:20260401T110000Z
UID:TALK245356@talks.cam.ac.uk
DESCRIPTION:We will look at the eigenvalue of the magnetic Laplacian in a 
 bounded domain in the plane\, with uniform magnetic field and Neumann boun
 dary conditions. This problem has been studied for a long time by physicis
 ts for its relevance to superconductivity\, but many mathematical question
 s remain open. While previous work has mainly been concerned with asymptot
 ic expansions for a large magnetic field\, there has been a recent focus o
 n explicit eigenvalue bounds.I will give an overview of joint work with Br
 uno Colbois\, Luigi Provenzano and Alessandro Savo\, in which we obtained 
 upper and lower bounds for the eigenvalues\, depending only on the value o
 f the magnetic field and a few geometric parameters of the domain. In part
 icular\, I will describe a step toward the proof of a reverse Faber-Krahn 
 inequality conjectured by S&oslash\;ren Fournais and Bernard Helffer. I wi
 ll also present the results of a joint work with Bernard Helffer\, which c
 onnects\, in the case of the disk\, the intensity of the magnetic field wi
 th the angular momentum of the first eigenfunction.&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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