Spectral properties of Maxwell operators

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• Francesco Ferraresso (Università degli Studi di Verona)
• Thursday 05 February 2026, 10:30-11:15
• Seminar Room 1, Newton Institute.

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GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

The Maxwell system (1865) in time-harmonic formulation has always an infinite dimensional kernel (given by gradient fields), even in bounded domains; therefore, the Maxwell essential spectrum is always not-empty, and many standard spectral theory techniques fail. Even more dramatically, dissipative Maxwell systems in bounded domains might have segments of essential spectrum along the imaginary axis.  I 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 domains $\Sigma_\epsilon = \Sigma \times (0, \epsilon)$, the eigenvalues of the Maxwell system converge to the eigenvalues of the Dirichlet Laplacian 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 dissipative Maxwell systems, featuring non-constant, discontinuous, complex-valued coefficients. Based on joint work with S. B\”ogli (Durham), M. Marletta (Cardiff), L. Provenzano (Sapienza Rome) and C. Tretter (Bern).

This talk is part of the Isaac Newton Institute Seminar Series series.

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