# Maas Group

## Stochastic Analysis

Jan Maas is a mathematician working in probability theory and mathematical analysis. His research focuses on stochastic processes, which describe a wide variety of real-world systems subject to randomness or uncertainty.

A major source of inspiration comes from optimal transport, a classical subject in engineering and economics concerning the optimal allocation of resources. In recent years optimal transport has been used to establish deep and fascinating connections between seemingly unrelated problems in mathematics, involving curvature of metric measure spaces, gradient flow structures for nonlinear partial differential equations (PDEs), and many other applications. Maas' current research aims to extend techniques from optimal transport into new directions, and to apply these ideas to problems involving discrete stochastic systems, chemical reaction networks, and quantum mechanics.

Another main focus is on stochastic PDEs, which are commonly used to model high-dimensional random systems in science and engineering. The rigorous study of these equations often poses great difficulties, since solutions to interesting equations are frequently so irregular that existing mathematical methods cannot be applied. In many situations it is even already very challenging to find an appropriate notion of solution. One of the aims is to develop robust mathematical techniques for the study of such equations. These techniques lead to new insights in the underlying models, and also allow one to obtain convergence results for discrete approximating systems.

#### Contact

Jan Maas

Institute of Science and Technology Austria (IST Austria)

Am Campus 1

A – 3400 Klosterneuburg

Phone: +43 (0)2243 9000-6101

E-mail: jan.maas@
ist.ac.at

#### Assistant

Jessica de Antoni Phone: +43 (0)2243 9000-1178 E-mail: jessica.deantoni@ist.ac.at

**Team**

- Dominik Forkert, PhD student
- Mate Gerencser, Postdoc
- Peter Nejjar, Postdoc
- Giovanni Zanco, Postdoc

#### Selected Publications

- Hairer M, Maas J, Weber H. 2014. Approximating rough stochastic PDEs.Comm. Pure Appl. Math. 67 (5), 776-870.
- Carlen E, Maas J. 2014. An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy. Comm. Math. Phys. 331 (3), 887-926.Erbar M, Maas J. 2012. Ricci curvature of finite Markov chains via convexity of the entropy. Arch. Ration. Mech. Anal. 206 (3), 997-1038.
- Hairer M, Maas J. 2012 A spatial version of the Itô-Stratonovich correction. Ann. Probab. 40 (4), 1675–1714.
- Maas J. 2011. Gradient flows of the entropy for finite Markov chains. J. Funct. Anal. 261 (8), 2250-2292.

#### Career

Since 2014 Assistant Professor, IST Austria

2009-2014 Postdoc, University of Bonn, Germany

2009 Postdoc, University of Warwick, UK

2005-2009 PhD in Applied Mathematics, TU Delft, 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