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