Organisation/Company: Aix-Marseille Université
Research Field: Mathematics » Applied mathematics, Mathematics » Geometry, Mathematics » Mathematical analysis
Researcher Profile: First Stage Researcher (R1)
Country: France
Application Deadline: 3 Feb 2025 - 11:00 (UTC)
Type of Contract: Temporary
Job Status: Full-time
Hours Per Week: 38
Is the job funded through the EU Research Framework Programme? Not funded by a EU programme
Is the Job related to staff position within a Research Infrastructure? No
Offer Description RESEARCHER PROFILE: PhD/R1: First stage Researcher
RESEARCH FIELD(S): Mathematics
MAIN SUB RESEARCH FIELD OR DISCIPLINES: 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 at 12:00
ENVISAGED STARTING DATE: 01/Sept/2025
ENVISAGED DURATION: 36 months
JOB NOT FUNDED THROUGH AN EU RESEARCH FRAMEWORK PROGRAMME
QUALIFICATIONS: 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:
One letter of recommendation from a master's teacher which he/she must send directly by email.
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