Dear all,

Here is the announcement of two MAP seminars for the upcoming week.

⟶ Date: Tuesday 28th May, 14:30-16:30

⟶ Where: Aula Riunioni (Pisa) and online on Google Meethttps://seminarimap.wixsite.com/seminarimap/2023-2024-1/rana-badreddine

⟶ Schedule:

* 14:30 - Rana Badreddine - Zero dispersion limit of the Calogero-Moser DNLS equation; * 15:30 - Marc Rouveyrol - Spectral estimate for the Laplace operator on the hyperbolic half-plane.

More information are provided below.

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⟶ Speaker 1: Rana Badreddine (Université de Paris-Saclay)             link: Rana Badreddine/seminarimaphttps://seminarimap.wixsite.com/seminarimap/2023-2024-1/rana-badreddine

⟶ Title: Zero dispersion limit of the Calogero-Moser DNLS equation

⟶ Abstract: We introduce the Calogero-Moser derivative nonlinear Schrödinger equation. We study its semiclassical limit by establishing the existence of a weak limit solution when we neglect the dispersion part of the equation. This weak limit solution will be identified explicitly. In a subsequent step, we explore the relationship between this weak limit and the branches of the multivalued solution of the Burgers equation. Finally, we derive a maximal principle that governs this weak limit solution.

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⟶ Speaker 2: Marc Rouveyrol (Université de Paris-Saclay)             link: Marc Rouveyrol/seminarimaphttps://seminarimap.wixsite.com/seminarimap/2023-2024-1/marc-rouveyrol

⟶ Title: Spectral estimate for the Laplace operator on the hyperbolic half-plane

⟶ Abstract: Spectral estimates on manifolds have been studied since the end of the 80s, in connection with spectral geometry and control of the heat equation. After introducing some background and motivation, I will present an original spectral estimate result on the hyperbolic half-plane, the first of its kind in a non-Euclidean setting. If time allows, the proof will be discussed along with possible generalizations. The tools involved come from spectral theory, harmonic analysis, control of PDEs and basic geometry.

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We remind you that these seminars are addressed to everyone: the first half is dedicated to introducing concepts and tools, while the second half focuses on research topics.

For more information, check our website: https://seminarimap.wixsite.com/seminarimap

See you soon,

The organizers: Jeremy Mirmina Filippo Paiano Mario Rastrelli Leonardo Roveri

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