PhD thesis offer: Dirac type operators in the presence of non-trivial geometries

• Location: Université de Bordeaux, Institut de mathématiques de Bordeaux
• Duration: 36 months
• Start date: september or october 2026
• Application deadline : May 31, 2026

The purpose of this thesis is to contribute to the mathematical study of Dirac-type operators in the presence of particular geometries (curved interfaces, magnetic or singular perturbations, domains with boundaries, domains with corners, etc.). For Dirac-type models drawn from condensed matter physics, our aim is to give a more complete spectral description (band functions) of reference operators (free operators) and then in the presence of a boundary, perturbations or interfaces. We will also focus on the fine propagation phenomena of edge states produced in this media, giving a general interpretation of edge states in terms of coherent states propagation and Wigner measures.

Description: Sujet de thèse

Application: Le dossier de candidature doit contenir les pièces justificatives suivantes :

• Un curriculum vitae détaillé du candidat avec les résultats académiques.
• Une lettre de motivation du candidat.
• Le titre et le résumé du sujet de recherche sélectionné.
• Les relevés de notes universitaires (ou du parcours d’ingénieur) de Master 1 et de Master 2 faisant apparaître les classements du candidat.
• Une attestation de réussite au Master ou équivalent, le cas échéant.
• Lettres de recommandation (responsable du stage de Master, responsable Master, etc.).
• Un exemplaire électronique du mémoire de Master (si disponible).

Les documents sont à envoyer, avant le 31 mai 2026, aux deux adresses suivantes avec dans l’objet « Application PhD Dirac operator »:

brahim.lounis@u-bordeaux.fr

vincent.bruneau@u-bordeaux.fr

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Postdoc offer – Spectral analysis of PDEs / Dirac operator

• Location: Université de Bordeaux
• Duration: 12 months
• Start date: september or october 2026
• Application deadline : January 31, 2026

A postdoctoral research position is open at Université of Bordeaux within the IMB in the team PDE-Mathematical Physic. The postdoc position is funded by the ANR- project SpecDiMa dedicated to the analysis of PDE and spectral analysis of operators in the broad sense (spectral asymptotics, scattering theory, resonance theory, semiclassical analysis, microlocal analysis etc.). It aims to contribute to the mathematical description of new phenomena in condensed matter physics associated with Dirac-type systems and to explore the mathematical questions raised. An important objective of these models is to reveal “edge states” which propagate either along the edge of the domain or at an interface created by a variable mass or an electric/magnetic potential.

The person recruited will contribute to one of the following objectives of the project:

1. Band functions of fibered operators: Periodic operators with conical band functions and operators invariant in one direction (Dirac “waveguide”). Description of their band functions (or dispersion curves) as well as the associated eigenvectors.
2. Edge states: For some reference operators without perturbation, study of edge states and their localizations. Develop a more general interpretation of edge states in terms of coherent states propagation and Wigner measures for bent interfaces.
3. Influence and interaction of perturbations/impurities: effect of perturbations (electromagnetic potential, obstacle) on the ideal operators, study of the eigenvalues, resonances, scattering matrix and spectral shift function. In addition, study of the stability of edge currents The person recruited will work under the supervision of one/several members of the project.

People interested should apply by sending an email to : Vincent.Bruneau@math.u-bordeaux.fr with the subject line “Application postdoc SpecDiMa”, and containing a single PDF document including the elements below:

• Cover letter
• CV and list of publications
• Research description (maximum 2 pages)

Support letters can be sent at the same address.