Associate Professor of Mathematics, UCLA
Interacting stochastic systems
From microscopic randomness to macroscopic laws — in particles, spins, markets, and AI agents.
I study how many interacting random or imperfect components produce reliable collective behaviour. My tools come from probability, statistical mechanics, optimal transport, PDE, and data-driven computation.
I joined UCLA's Department of Mathematics in January 2016. Before that I held postdoctoral positions at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Stanford University, and the Simons Laufer Mathematical Sciences Institute (SLMath, formerly MSRI). I did my PhD with Felix Otto.
The common theme in my work is interaction. Many simple objects — particles, spins, random height functions, market orders — can produce surprisingly stable macroscopic behaviour, and I try to understand when this happens, how fast it happens, and how robust the resulting laws are: a noisy microscopic system, on the right scale, behaves like the solution of a heat equation; random height functions concentrate on predictable limit shapes; the trades of many small agents aggregate into a market price.
Lately the same theme has pulled me into AI for mathematics. With my student Maciej Głuchowski I developed AGRADE, an automated, multi-agent AI grading tool currently piloted in the UCLA Mathematics Department. A network of language models, structured to critique and repair one another, can be far more reliable than any one of them on its own — which is, in a different language, the same question that drives much of my mathematical work: how does reliable macroscopic behaviour emerge from many unreliable interacting parts?
Current PhD students.
Edward Athaide,
Maciej Głuchowski.
Former PhD students.
Tianqi Wu, Andrew Krieger, Younghak Kwon.
Hydrodynamic limits, convergence to equilibrium, functional inequalities, phase transitions, metastability, and variational principles for random maps.
Hydrodynamic limit Functional inequalities Spin systems Metastability Random maps Quantitative CLTs
Market microstructure, aggregation of orders into prices, market-dynamical entropy, non-conservative optimal transport, and operator learning for price impact and execution.
Multi-agent systems for grading, proof critique, repair, and verification.
Current talk topics:
Georg Menz is an Associate Professor of Mathematics at UCLA. His research studies interacting stochastic systems, using tools from probability, statistical mechanics, optimal transport, PDE, and computation. His recent work connects classical problems such as hydrodynamic limits and functional inequalities with market microstructure, non-conservative optimal transport, and AI-assisted mathematical verification.
Email. gmenz@g.ucla.edu
Office.
520 Portola Plaza
Math Sciences Building 6363, Office 6148
Los Angeles, CA
Mail.
UCLA Mathematics Department
Box 951555
Los Angeles, CA 90095-1555