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

If you are interested in writing a Bachelor’s or Master’s thesis, feel free to get in contact.

news

Sep 18, 2026	Workshop update: I participate in the Optimisation and Learning in Games Workshop, held at the Technical University of Munich on September 25, 2026.
Sep 10, 2026	Conference update: Our poster, Support Collapse from Entropic First-Order Stationarity in First-Price Auctions, has been accepted for presentation at SAGT 2026. The work is co-authored by Martin Bichler, Philip Hierhager, and Jan Hoehener.
Jun 23, 2026	Workshop update: I participate in the Summer Workshop in the Calculus of Variations, held at the Technical University of Munich from July 20–23, 2026.

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.