For a few years, I'll be focusing on the following topics:
Generative AI and diffusion models (via the lens of optimal transport, control, stochastic analysis, and rough path theory)
Reading: PeydiffTrans, GenAIM-CalcI, GenAIM-CalcII, RoughPathsIn-ML
Optimal transport (theory and applications) and Schrödinger bridges;
Reading: PeyOT4ML, LeoSBOT, CheGeoPav-I, CheGeoPav-II,
Mean field games and their numerical treatment via RL;
Reading: CarLau-MFRL, Mert-LiG, Lau-MFG-Num, Lau-DL-MFG, Lau-OT-MFG
Game theory in control and learning
Reading: Lau-ConGames, ZuaML-and-Con
Optimization and optimal control theory; numerical methods (robust, stochastic, sparse, bi-level etc.);
Reading: NumOptCon, BiLevOptCon, FlemRichSOC
PDE-constrained optimizaiton and control via operator-theoretic techniques from scientific ML;
Reading: NeurOps, PeyPDE4ML
Anomaly/attack detection in cyber-physical systems;
Reading: DetectionTheo
Multi-agent systems and control perspective of transformers
Reading: MathTransformers, MeanFieldTrans, MeasIntTrans, MultAgeMeasEvol
Motion planning under stochastic uncertainties.
If you are interested in working on problems related to any of these areas, or on closely related topics, please feel free to get in touch. Some projects require a sufficient mathematical background, while others may be accessible with more modest prerequisites. You may read the articles linked under a specific topic for a general introduction. In any case, the prerequisites can be learned along the way. I'm happy to discuss possible problems, the necessary background, and how one might get started. The specific preparation needed will depend on the problem.