BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Spectral properties of Maxwell operators - Francesco Ferraresso (U
 niversità degli Studi di Verona)
DTSTART:20260205T103000Z
DTEND:20260205T111500Z
UID:TALK239830@talks.cam.ac.uk
DESCRIPTION:The Maxwell system (1865) in time-harmonic formulation has alw
 ays an infinite dimensional kernel (given by gradient fields)\, even in bo
 unded domains\; therefore\, the Maxwell essential spectrum is always not-e
 mpty\, and many standard spectral theory techniques fail. Even more dramat
 ically\, dissipative Maxwell systems in bounded domains might have segment
 s of essential spectrum along the imaginary axis.&nbsp\;\nI will discuss a
  few results regarding the spectrum of the time-harmonic Maxwell system in
  domains with interesting geometry. For product domains\, I will show that
  the classical TE-TM modes decomposition of the eigenvalues generalises to
  the "curved case"\, where the domain is in the form $\\Sigma \\times I$\,
  $\\Sigma$ being a two-dimensional manifold. In particular\, for thin doma
 ins $\\Sigma_\\epsilon = \\Sigma \\times (0\, \\epsilon)$\, the eigenvalue
 s of the Maxwell system converge to the eigenvalues of the Dirichlet Lapla
 cian on $\\Sigma$\, as $\\epsilon \\to 0^+$. In unbounded domains\, I will
  show a few examples showing that\, depending on the geometry at infinity\
 , the essential spectrum of the Maxwell system might assume very different
  shapes. Time-permitting\, I will generalise this picture to the case of d
 issipative Maxwell systems\, featuring non-constant\, discontinuous\, comp
 lex-valued coefficients.\nBased on joint work with S. B\\"ogli (Durham)\, 
 M. Marletta (Cardiff)\, L. Provenzano (Sapienza Rome) and C. Tretter (Bern
 ).
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR