PhD student in mathematics, specifically partial differential equations and spectral theory: three-year position

RESEARCHER PROFILE: PhD/R1: First stage Researcher                   
RESEARCH FIELD(S)1: Mathematics
MAIN SUB RESEARCH FIELD OR DISCIPLINES1: Partial differential equations, spectral theory, asymptotic analysis, differential geometry, Finite elements

JOB /OFFER DESCRIPTION 
In the framework of the ANR project “Geometrically Dependent Hamiltonian” (GeoDHa), we are hiring a Ph.D. student. The selected Ph.D. student will work at the “ Institut de Mathématiques de Marseille” in the Applied Analysis team, located on the Saint-Charles campus. This team focuses on the study of Partial Differential Equations (PDE) either from a theoretical or numerical standpoint.

The main objective of the GeoDHa project is to investigate the impact of geometry on the energy levels of quantum mechanical models that incorporate the effects of special relativity. From a mathematical standpoint, this involves finding eigenpairs of a first-order elliptic PDE with boundary conditions ensuring the self-adjointness of the problem. The overall objective of the thesis is to understand how such eigenpairs depend on the geometry of the domain in which the PDE is posed. While answering this question in full generality is challenging, there are simpler cases where a precise description of the spectrum is possible, providing clear insights into the impact of the geometry. One example of such a situation is to consider a family of domains depending on a parameter which degenerates to a submanifold of the ambient Euclidean space when the parameter goes to zero. In this setting it is possible to obtain asymptotic expansions for the eigenpairs where the geometry appears explicitly in the leading terms of the asymptotic expansion.

Several problems in this spirit, approached from different perspectives, could be explored by the Ph.D. student, either from a theoretical or numerical standpoint, depending on her/his interests. 

TYPE OF CONTRACT: TEMPORARY / JOB STATUS: FULL TIME        
APPLICATION DEADLINE: 03/02/2025 & TIME 12:00
ENVISAGED STARTING DATE: 01/Sept/2025
ENVISAGED DURATION: 36 months
JOB NOT FUNDED THROUGH AN EU RESEARCH FRAMEWORK PROGRAMME

WORK LOCATION(S): Institut de Mathématiques de Marseille, Campus Saint-Charles, 13003 Marseille

WHAT WE OFFER: 
Salary: 2100 euros gross per month

Additional information: The Euraxess Center of Aix-Marseille Université informs foreign visiting professors, researchers, postdoc and PhD candidates about the administrative steps to be undertaken prior to arrival at AMU and the various practical formalities to be completed once in France: visas and entry requirements, insurance, help finding accommodation, support in opening a bank account, etc. More information on AMU EURAXESS Portal 

QUALIFICATIONS, REQUIRED RESEARCH FIELDS, REQUIRED EDUCATION LEVEL, PROFESSIONAL SKILLS, OTHER RESEARCH REQUIREMENTS (years of research experience (max. 3000 characters) 
A master degree in mathematics and applications, with an emphasis on analysis. Knowledge of basic operator theory, spectral theory, differential geometry and/or of finite elements method would be a plus but is not mandatory.

Soft skills: Skills in English or French language.

REQUESTED DOCUMENTS OF APPLICATION, ELIGIBILITY CRITERIA, SELECTION PROCESS

• Academic CV: In a pdf file (to thomas.ourmieres-bonafos@univ-amu.fr)
• One letter of recommendation from a master’s teacher which he / she must sent directly by email.

HOW TO APPLY: thomas.ourmieres-bonafos@univ-amu.fr