Maas Group

Stochastic Analysis

Airplane turbulence, stock rate fluctuations, and epidemic spreading are examples of highly irregular real-world phenomena subject to randomness, noise, or uncertainty. Mathematician Jan Maas develops new methods for the study of such random processes in science and engineering.

Random processes are often so irregular that existing mathematical methods are insufficient to describe them accurately. The Maas group combines ideas from probability theory, mathematical analysis, and geometry to gain new insights into the complex behavior of these processes. Their recent work has been inspired by ideas from optimal transport, a subject originating in economics and engineering that deals with the optimal allocation of resources. The Maas group applies these techniques to diverse problems involving complex networks, chemical reaction systems, and quantum mechanics. Another research focus is stochastic partial differential equations. These equations are commonly used to model high-dimensional random systems in science and engineering, ranging from bacteria colony growth to weather forecasting. The Maas group develops robust mathematical methods to study these equations, which is expected to lead to new insights into the underlying models.

Group Leader


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Team


Current Projects

Homogenization of discrete optimal transport | Curvaturedimension criteria for Markov processes | Gradient flow structures in dissipative quantum systems


Publications

Forkert DL. 2020. Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains, IST Austria, 154p. View

Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. Journal des Mathematiques Pures et Appliquees. View

Zhang H. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. View

Gerencser M. Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. View

Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378. View

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Career

since 2014 Assistant Professor, IST Austria
2009 – 2014 Postdoc, University of Bonn, Germany
2009 Postdoc, University of Warwick, UK
2009 PhD, Delft University of Technology, The Netherlands


Selected Distinctions

2016 ERC Starting Grant
2013 – 2014 Project Leader in Collaborative Research Centre “The mathematics of emergent effects”
2009 – 2011 NWO Rubicon Fellowship


Additional Information

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