2-3 Dec 2019 Marseille (France)

Trending topics in spectral theory

The workshop, which is part of the "Journées thématiques d'Analyse Appliquée" series, will take place at the FRUMAM, on the Saint-Charles campus of the University Aix-Marseille, on Monday, 2 December 2019, in the afternoon and on Tuesday, 3 December 2019, in the morning.

The workshop will consist of a two hour mini-course, given by Monique Dauge (Rennes), three 45-minutes talks, delivered by Vladimir Lotoreichik (Prague), Nicolas Raymond (Angers), and Eric Soccorsi (Marseille) and a 30-minutes talk delivered by Sylvain Zalczer (Toulon).

The participation to the workshop is free of charge. Registration for the lunch on Tuesday is now closed, but participants are welcome to join the workshop without signing up.

 

Schedule

Monday, 2 December 2019

The talks will take place in the seminar room on the 3rd floor.

13:30-14:00: Welcome

14:00-14:45: Monique Dauge

Title: An introduction to elliptic corner problems via the example of polygonal metamaterials (1)

Abstract can be found here and slides can be found here.

15:00-16:00: Monique Dauge

Title: An introduction to elliptic corner problems via the example of polygonal metamaterials (2)

Abstract can be found here and slides can be found here.

16:15-17:00: Eric Soccorsi

Title: Multidimensional Borg-Levinson inverse spectral problems

Abstract: This talk is concerned with the uniqueness and the stability issues in the inverse problem of determining the electric potential of the multidimensional Laplace operator (dimension 2 or greater) by partial knowledge of the boundary spectral data. As an application, the multidimensional Borg-Levinson inverse spectral theory is used to retrieve the potential from partial parabolic Dirichlet-to-Neumann operator measured at a given time.

 

Tuesday, 3 December 2019

The talks will take place in the seminar room on the 2nd floor.

9:15-9:45: Sylvain Zalczer

Title: Spectral localization for random Dirac operators


Abstract: The Dirac operator is a first-order differential operator acting on $L^2(\mathbb{R}^2,\mathbb{C}^2)$. We prove spectral localization at the edge of the bands for a gapped Dirac operator perturbed by a random potential.

10:15-11:00: Vladimir Lotoreichik

Title: Optimization of principal Robin eigenvalues on 2-manifolds and unbounded cones.

Abstract can be found here.

11:10-11:55: Nicolas Raymond

Title: A first formula of pure magnetic tunnel effect.

Abstract: The semiclassical magnetic Neumann Schrödinger operator on a generic, smooth, bounded, and simply connected domain of the Euclidean plane is considered. When the domain has a symmetry axis, the semiclassical splitting of the first two eigenvalues is analyzed. 

The first explicit tunneling formula in a pure magnetic field is established. The analysis is based on a pseudo-differential reduction to the boundary and the proof of the first known optimal purely magnetic Agmon estimates. 

Joint work with V. Bonnaillie-Noël and Frédéric Hérau

 

Organizers: Thomas Ourmières-Bonafos, Enea Parini

e
Online user: 1