Description of the thesis topic

We propose a general mathematical theory of how gene expression fluctuations propagate from their sources (transcription sites) to the embryo's phenotype represented by the gene products spatio-temporal patterns. Markov processes are used as a basic tool (Gillespie algorithm) and spatial dependence is taken into account. Limit theorems will be proved to justify the use of simplified models based on PDEs, stochastic PDEs and Piecewise Deterministic Markov Processes. These mathematical models are well suited to numerical simulations, this will allow to validate them by comparison with available biological data.

Work Context

The thesis will be carried out at IRMAR, a mathematics laboratory located on the Beaulieu and Ker Lann campuses in Rennes. This is a multidisciplinary collaboration with the LPHI in Montpellier. The PhD student will therefore travel to Montpellier on a regular basis.
Expected skills: Master's degree in Mathematics, ability to write in French and English, autonomy.

Constraints and risks

nothing to report