Post-doc

• Post-doc offer : The 2-year post-doc project (starting Sept. 2025), co-supervised by Y. Achdou (Paris-Cité) and P. Cardaliaguet (Paris Dauphine) is within the framework of the ANR COSS (COntrol on Stratified Structures (COSS)) and concerns questions of Hamilton-Jacobi (HJ) equations and scalar conservation laws (SCL) on junctions, their optimal control, and their numerical approximation. Motivated in particular by traffic flow models, the project will consist of better understanding the conditions to be put at the junction (notion of admissible germ), and how to choose these conditions (optimal control), so as to optimize certain criteria (optimality conditions, bang-bang properties of optimal control, corresponding infinite-dimensional HJ equations). Another aspect of the project is the mean field counterpart of these questions: at least in simple cases, it is known that these equations (HJ and SCL on junctions) can be obtained as limits of large particle systems (interpreted as vehicles). This micro-macro passage to the limit is still widely open for general junctions, although it is key for better understanding these equations and justifying the conditions at the junction. A second aspect of the project will therefore consist of understanding this micro-macro derivation in currently open cases (for example 2 incoming and 2 outgoing routes). In parallel, it will be possible to study how the optimal control of a large number of vehicles on a junction gives rise to an optimal control at the junction for HJ or SCL equations after a micro-macro passage (Mean field control). The two aspects of the project may be tackled theoretically or numerically. REF : Cardaliaguet, P., Souganidis, P. E. (2024) An optimal control problem of traffic flow on a junction. arXiv preprint arXiv:2312.15418. ESAIM-cocv 30 (2024) 88. Cardaliaguet, P., Forcadel, N., and Monneau, R. (2024). A class of germs arising from homogenization in traffic flow on junctions. arXiv preprint arXiv:2311.11709. J. Hyperbolic equations, 21(02), 189-254.

PhD theses

• PhD offer on "Homogénéisation d’équations de Hamilton-Jacobi conduisant à des problèmes stratifiés".
• At the Department of Mathematics of the INSA Rouen Normandie is open a call for a PhD position on the subject: Trafic flow analysis and modelling. (open from July 15 to November 15)
• At the Department of Mathematics of the University of Trento is open a call for a PhD position on the subject: Mathematical modeling, analysis and control of flows in Euclidean environments and on networks: single agents and masses of agents.