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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.




Team


Current Projects

Optimal transport on random networks | Rates of convergence for evolutionary dynamics | Entropy inequalities and dissipative quantum systems


Publications

Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria. View

Brigati G, Dolbeault J, Simonov N. 2024. Stability for the logarithmic Sobolev inequality. Journal of Functional Analysis. 287(8), 110562. View

Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 63(6), 153. View

Dello Schiavo L, Maas J, Pedrotti F. 2024. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 377(6), 3779–3804. View

Volberg A, Zhang H. 2024. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. 389, 1657–1676. View

View All Publications

ReX-Link: Jan Maas


Career

Since 2020 Professor, Institute of Science and Technology Austria (ISTA)
2014 – 2020 Assistant Professor, Institute of Science and Technology Austria (ISTA)
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

Jan Maas website
Mathphys Analysis Seminar website
Mathematics at ISTA



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