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Explore the intricacies of geometric degeneration and its impact on the Laplace spectrum in this comprehensive seminar from the "Spectral Geometry in the clouds" series. Delve into the classical question of how the spectrum of a geometric object behaves during degeneration, examining both singular and analytic perturbation theory approaches. Discover the fundamental differences between these methods and learn about well-established and recent findings in the field. Gain insights into the relationship between spectral behavior and semiclassical concentration properties, and understand their applications to spectral simplicity in simple shapes. Drawing from joint work with C. Judge, this hour-long lecture by Luc Hillairet from Université D'Orléans offers a deep dive into spectral tools for geometric degeneration, providing valuable knowledge for researchers and enthusiasts in spectral geometry and related mathematical disciplines.
