Heat flow in random and homogenized materials

A three-year PhD position in Mathematics is available at Universite Polytechnique Hauts-de-France (UPHF) within the context of the Chaire de Professeur Junior project "Mathematical modeling and optimisation of additive manufacturing of ceramics", funded by Agence Nationale de Recherche.

This is a pure research position with no teaching duties. The salary will be the statewide sanctioned salary for PhD students (2,200€ gross per month in 2025; 2,300€ gross per month from 2026). There are generous funds for research visits, conferences and guests.

The CERAMATHS laboratory is a research unit of UPHF, consisting of the department of mathematics (DMATHS) and the department of material sciences and processes (DMP), working on ceramics research. This combines the advantage of an environment suitable for pure mathematical research with organizational proximity to applied research.

The project will relate to the mathematical theory of heat flow in porous and granular materials which are ubiquitous in material science. While being crucial for applications such as sintering and
3D printing, understanding the heat flow poses massive challenges. Randomness at microscopic scales can have profound implications, yet has remained elusive in existing models.

In this project, we aim to advance the theory of heat diffusion in such materials by combining recent progress in stochastic homogenization with techniques developed in the context of the multi-scale analysis for random Schrodinger operators, and percolation.

Candidates are expected to have:

• a master's degree or equivalent in Mathematics (defense by Fall 2025),
• a background in analysis, mathematical Physics or probability theory,
•  eagerness to quickly engage with a new topic,
• willingness to collaborate with both theorists and applied researchers.

Knowledge in Anderson localization, homogenization or percolation is a plus but not required. Profficiency in French is not necessary but taking up language classes upon arrival as offered by UPHF is strongly encouraged.