Le séminaire des doctorants se propose de fournir aux doctorants une occasion de s'ouvrir aux autres domaines des mathématiques que le leur. A chaque séance, un intervenant réalise un exposé sur un fait standard de leur domaine d'étude, de niveau adapté à l'ensemble des doctorants.

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The PhD students seminar aims to provide PhD students with an opportunity to explore other areas of mathematics beyond their own. At each session, a speaker gives a presentation on a standard topic in their field of study, at a level suitable for all doctoral students.

In 1966, Mark Kac famously asked: “Can one hear the shape of a drum?” — that is, can the geometry of a domain $\Omega \subset \mathbb{R}^d$ be determined from the spectrum of the Dirichlet Laplacian on $\Omega$? The answer, known since 1985, is no, where Sunada gave a method for constructing isospectral Riemannian manifolds. Nevertheless, the spectrum does encode significant geometric information. In this talk, we will explore the deep connections between geometry and spectral theory, discussing what can (and cannot) be “heard” from the eigenvalues of a drum.