Matthias Rakotomalala, Dr.

Postdoctoral Researcher in Mathematics at the Technical University of Munich

I am currently a postdoctoral researcher at the Technical University of Munich, affiliated with the Chair of Analysis and Modelling (Prof. Johannes Zimmer). I defended my PhD in Applied Mathematics on September 3, 2025, at École polytechnique (CMAP), under the supervision of Dr. Charles Bertucci (Chargé de recherche, CNRS).

My thesis, On some systems of partial differential equations of the mean-field type, is available here.

My research focuses on the analysis of partial differential equations and stochastic differential equations. It orbits around understanding the emergence of collective behaviors in mean-field models of large populations of interacting agents or particles, with applications in biology, economics, and, more recently, physics.

Monte Carlo particle simulations of the model introduced in [3], applied to trail pattern formation in ant chemotaxis. Orange arrows represent ants, and the concentration of pheromones is shown in blue.

Publications

[4] Existence and dimensional lower bound for the global attractor of a PDE model for ant trail formation, with Oscar de Wit, arXiv preprint, arXiv:2504.01765, 2025.

[3] Curvature in chemotaxis: A model for ant trail pattern formation, with Charles Bertucci and Milica Tomašević, Mathematical Models and Methods in Applied Sciences, 35(12), 2695–2740, 2025. arXiv-version

[2] Strategic geometric graphs through mean field games, with Charles Bertucci, SIAM Journal on Control and Optimization 63.4: 2577-2604, 2025. arXiv-version

[1] A practical global existence and uniqueness result for stochastic differential equations on Riemannian manifolds of bounded geometry, arXiv preprint, arXiv:2404.12985, 2024.

Contact

matthias[dot]rakotomalala[at]tum[dot]de