Philip Hierhager

I am a researcher at the Technical University of Munich working on optimization, variational inequalities, dynamical systems, learning in games, stochastic approximation, and measure-valued methods.

Research Interests

Optimization and variational inequalities
Dynamical systems and Lyapunov methods
Learning in games and multi-agent systems
Stochastic approximation and online learning
Infinite-dimensional and measure-valued methods
Newtonian and Hamiltonian dynamics on metric spaces

Thesis Supervision

I supervise Bachelor’s and Master’s theses in optimization, dynamical systems, learning theory, game theory, stochastic algorithms, and formalization of mathematical methods. A list of open topics with downloadable PDF proposals is available on the Theses page.

news

Jun 01, 2026	New preprint: Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs is now available on arXiv.

selected publications

arXiv

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs

Philip Hierhager

2026

Abs

This paper studies deterministic Hamiltonian dynamics on finite metric graphs. Since energy conservation alone does not determine how a trajectory continues through a branching vertex, the paper introduces energy-preserving vertex scattering maps. The resulting edge-and-vertex dynamics define a global measurable flow that preserves energy and the quotient Liouville measure.