Dear all,

We remind you about tomorrow's seminars.

⟶ *Date:* Tuesday 28th May, 14:30-16:30

⟶ *Where: *Aula Riunioni (Pisa) and online on Google Meet https://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 is provided below.

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⟶ *Speaker 1:* Rana Badreddine (Université de Paris-Saclay) link: Rana Badreddine/seminarimap https://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/seminarimap https://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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