MAA 525 – Mean-field particle systems and their limits to non-local PDEs

This is a self-study course consisting of video lectures and lecture notes. In addition, we offer weekly in-person sessions where you can ask questions and discuss the material. These sessions will be led by Lukas Bol and will take place on Tuesdays at 13:45 in Room C 4.01 (B6 28, Bauteil C). The first session, on 8 September 2026, will be a brief introductory meeting to discuss course arrangements. Regular content sessions will then begin on 15 September 2026.

Please use this link to enter the ILIAS group where we will upload the materials.

Exam form: Oral (by arrangement)
Language: English
Prerequisites: Analysis I and II, Linear algebra I, Probability I

It is a master's course, however, all bachelor students who have already had “Analysis I and II” are welcome to join.

Aim of module:

Rigorous derivation of mean-field type PDEs. 

Topics include:
• Basic existence results for ODE and SDE
• Well-posedness theory of mean-field type nonlocal PDEs
• Entropy estimates for PDEs
• Derivation of kinetic mean-field equation from N-particle dynamical system.
• Derivation of diffusion-aggregation equation