
Benjamin Gess

Professor
TU Berlin and MPI MiS
Research profile
Benjamin Gess leads SAiS across TU Berlin and the Max Planck Institute for Mathematics in the Sciences. His research develops analytical and probabilistic methods for nonlinear PDEs, stochastic PDEs and interacting systems, with applications ranging from fluctuating hydrodynamics to machine learning.
Research areas
Nonlinear PDEs · SPDEs · Stochastic Dynamics · Numerics · Machine Learning · Non-equilibrium Statistical Mechanics, Interacting Particle Systems and Fluctuating Hydrodynamics · Stochastic Fluid Dynamics · Sampling
Five research keywords
conservative SPDEs · nonlinear diffusion · large deviations · interacting particle systems · stochastic dynamics
Contact and links
Public email
Institutional email: information to be provided by the member.
Institution
TU Berlin and MPI MiS
Academic links
Curriculum vitae
| Date | Appointment / education |
|---|---|
| 2024–present | W3 Professor, Technische Universität Berlin. |
| 2021–present | Research group leader, Stochastic Analysis in the Sciences, Max Planck Institute for Mathematics in the Sciences. |
| 2019–2024 | W3 Professor, Bielefeld University. |
| 2016–2021 | Max Planck research group leader, Max Planck Institute for Mathematics in the Sciences. |
| 2013–2015 | Postdoctoral researcher, University of Chicago, supported by a DFG research fellowship. |
| 2012–2013 | Postdoctoral appointments at TU Berlin, Humboldt-Universität zu Berlin and Bielefeld University. |
| 2009–2011 | PhD in Mathematics, Bielefeld University; advisor: Michael Röckner; summa cum laude. |
| 2007–2008 | MSc in Mathematics, University of Warwick; with distinction. |
| 2004–2007 | Studies in Mathematics and Computer Science, University of Bonn. |
Publications
This catalogue contains all publications by the member, including work from before joining SAiS. Journal versions and preprints are maintained as one record per scientific work.
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Optimal regularity in time and space for stochastic porous medium equations
Published · The annals of probability, 50 (2022) 6, pp. 2288-2343. We prove optimal regularity estimates in Sobolev spaces in time and space for solutions to stochastic porous medium equations. The noise term considered here is multiplicative, white in time and coloured in…
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Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise
Published · Mathematics of computation, 92 (2023), pp. 1931-1976. In micro-fluidics not only does capillarity dominate but also thermal fluctuations become important. On the level of the lubrication approximation, this leads to a quasi-linear fourth-order parabolic equation for the film height…
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Well-posedness of the Dean–Kawasaki and the nonlinear Dawson–Watanabe equation with correlated noise
Published · Archive for rational mechanics and analysis, 248 (2024) 2, p. 20. In this paper we prove the well-posedness of the generalized Dean–Kawasaki equation driven by noise that is white in time and colored in space. The results treat diffusion coefficients that are only…
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Stochastic partial differential equations arising in self-organized criticality
Published · The annals of applied probability, 35 (2025) 1, pp. 481-522. We study scaling limits of the weakly driven Zhang and the Bak-Tang-Wiesenfeld (BTW) model for self-organized criticality. We show that the weakly driven Zhang model converges to a stochastic partial differential equation…
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Stabilization by transport noise and enhanced dissipation in the Kraichnan model
Published · Journal of evolution equations, 25 (2025) 2, p. 42. Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second order linear operator with possibly unstable eigenvalues on a smooth compact Riemannian manifold, it is shown…
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Numerical approximation of singular-degenerate parabolic stochastic PDEs
Published · IMA journal of numerical analysis, 44 (2024) 4, pp. 2090-2137. We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a…
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An Example of Intrinsic Randomness in Deterministic PDEs
Published · Stochastics and dynamics, 22 (2022) 7, p. 2240023. A new mechanism leading to a random version of Burgers’ equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood as an intrinsically…
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Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
Published · Archive for rational mechanics and analysis, 242 (2021) 1, pp. 179-234. We prove the existence of nonnegative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range…
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Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process
Published · Communications in mathematical physics, 407 (2026) 4, p. 74. In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs…
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Porous media equations with multiplicative space-time white noise
Published · Annales de l’Institut Henri Poincaré / B : Probabilites et statistiques, 57 (2021) 4, pp. 2354-2371. The existence of martingale solutions for stochastic porous media equations driven by nonlinear multiplicative space-time white noise is established in spatial dimension one. The Stroock-Varopoulos inequality is identified as a key tool…
Current SAiS projects
FluCo
Principal investigator of the ERC Consolidator Grant.
NumGM
Principal investigator of the DFG project with Gabriele Steidl.
CoScaRa project
Principal investigator in Priority Programme 2410.
CRC/TRR 388 project A11
Principal investigator.
Fluctuations and Control
MATH+ project with Peter K. Friz.
CRC 1283 project B01
Associated project.
Talks and posters
Selected recent talks are included below. Poster presentations have not been recorded separately.
| Date | Talk or event |
|---|---|
| 2026 | FOCM, Vienna — Thermodynamically Consistent and Positivity Preserving Discretization of the Stochastic Thin Film Equation. |
| 2026 | 15th AIMS Conference, Athens — Large Deviations for the Porous Medium Equation via Multiscale Integrability. |
| 2026 | Sorbonne Université, conference celebrating Felix Otto — Gradient-flow structures for porous-media equations, large deviations and multiscale analysis. |
| 2026 | STOCHASTICA SNIP seminar — Large Spikes in SGD: A Large-Deviations View of Catapults. |
| 2026 | SIAM Optimization Conference, Edinburgh — Large Spikes in SGD: A Large-Deviations View of Catapults. |
| 2026 | (Ir)Regularity @ Parma I — Optimal regularity for the nonlocal anisotropic porous-medium equation. |
| 2026 | MFO, Flows on Measure Spaces and Applications in Machine Learning — Effective fluctuating continuum models for stochastic gradient descent. |
| 2026 | MFO, Modern and Emerging Phenomena in Machine Learning — Large Spikes in SGD: A Large-Deviations View of Catapults. |
| 2026 | CoScaRa Annual Meeting, MPI MiS — Rough and nonlinear transport in stochastic fluid dynamics. |
| 2025 | Mathematics Colloquium, University of Freiburg — Fluctuations in continuum. |
| 2025 | Mathematics Colloquium, University of Augsburg — Fluctuations in continuum. |
| 2025 | Beijing–Hong Kong PDE Seminar — From large deviations around porous media to PDEs with irregular coefficients and gradient-flow structures. |
| 2025 | Workshop on Geometry, Topology, and Machine Learning, MPI MiS — Fluctuating continuum models for stochastic gradient descent on curved spaces. |
| 2025 | MFO, Probabilistic Perspectives in Neural Network-Based Machine Learning — Effective fluctuating continuum models for Riemannian stochastic gradient descent. |
| 2025 | TU Berlin semester opening — Fluctuations in continuum. |
| 2025 | MPI MiS CRC Day — Fluctuations and stochastic dynamics in singular and interacting systems. |
| 2025 | Langenbach Seminar, WIAS — From large deviations around porous media to PDEs with irregular coefficients and gradient-flow structures. |
| 2025 | 8th International Conference on Random Dynamical Systems, Konstanz — Effective fluctuating continuum models for stochastic gradient descent. |
| 2025 | SPP 2410 workshop, Clausthal — Path-by-path regularization by noise for scalar conservation laws. |
| 2025 | Conservation Laws and Non-reciprocity, Münster — Gradient-flow structures and large deviations for porous-media equations. |
| 2025 | École normale supérieure, Paris — Gradient-flow structures and large deviations for porous-media equations. |
| 2025 | Bielefeld University Uncertainty Colloquium — Taming uncertainty and profiting from randomness in machine learning. |
| 2025 | 60th Netherlands Mathematical Congress, plenary lecture — Fluctuations in continuum. |
| 2025 | TRR 388 opening conference, Berlin — Gradient-flow structures and large deviations for porous-media equations. |
| 2025 | Stochastic Equations and Particle Systems, Sapienza University of Rome — Gradient-flow structures and large deviations for porous-media equations. |
| 2025 | GPSD, Dresden — Effective fluctuating continuum models for SGD with small learning rate or in overparameterized limits. |
| 2025 | GPSD, Dresden — Landau–Lifshitz–Navier–Stokes equations: large deviations and the energy equality. |
| 2025 | Academy of Sciences and Literature — Fluctuations in continuum. |
| 2025 | ESI Vienna — Optimal regularity for the nonlocal anisotropic porous-medium equation. |
| 2024 | Cortona — Effective fluctuating continuum models for SGD with small learning rate or in overparameterized limits. |
| 2024 | EPFL Lausanne — Large deviations from porous media, gradient-flow structures and SPDEs. |
| 2024 | ETH Zurich, Modern Perspectives in Applied Mathematics — From large deviations around porous media to PDEs with irregular coefficients and gradient-flow structures. |
| 2024 | TU Delft, SPDEs Below Sea Level — Large deviations from porous media, gradient-flow structures and SPDEs. |
| 2024 | NorPDE, Oslo — Optimal regularity for the nonlocal anisotropic porous-medium equation. |
| 2024 | Hamburg Colloquium on Mathematical Statistics and Stochastic Processes — Large deviations from porous media and gradient-flow structures. |
| 2024 | Seoul National University Probability Seminar — Large deviations from porous media and gradient-flow structures. |
| 2024 | Imperial College London — Large deviations from porous media and gradient-flow structures. |
| 2024 | ESI Vienna — Large deviations from porous media and gradient-flow structures. |
| 2024 | CIRM Marseille — Large deviations from porous media and gradient-flow structures. |
Teaching
| Term | Course or seminar |
|---|---|
| Summer 2026 | Seminar: Mathematics of Machine Learning; Seminar: Stochastic Analysis in the Sciences. |
| Winter 2025/26 | Seminar: Mathematics of Machine Learning; Seminar: Stochastic Analysis in the Sciences. |
| Summer 2025 | Seminar: Mathematics of Machine Learning; Seminar: Stochastic Analysis in the Sciences. |
| Winter 2024/25 | Seminar: Mathematics of Machine Learning. |
| Winter 2023/24 | Seminar: Mathematics of Machine Learning. |
| Summer 2023 | Seminar: Mathematics of Machine Learning. |
| Winter 2022/23 | Analysis I; Mathematics of Machine Learning; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar. |
| Summer 2022 | Mathematics for Natural Sciences II; Mathematics of Machine Learning III; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar. |
| Winter 2021/22 | Analysis II; Mathematics of Machine Learning II; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar. |
| Summer 2021 | Analysis I; Mathematics of Machine Learning; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar. |
| Winter 2020/21 | IRTG lecture: Large Deviation Estimates; Selected Topics in Large Deviations Theory; Stochastic Analysis research group. |
| 2020 | Large Deviations II. |
| 2019/20 | Large Deviations for Stochastic PDE I; Stochastic Thin-Film Equations at MPI MiS and Bielefeld University. |
| 2019 | Introduction to Singular SPDEs and Stochastic Variational Inequalities, MPI MiS; Stochastic Variational Inequalities, Bielefeld University. |
| 2018/19 | Random Dynamical Systems and Stochastic Porous-Media Equations with Nonlinear Noise, MPI MiS and Bielefeld University. |
| 2018 | Optimal Regularity Theory for the Porous-Medium Equation, MPI MiS; Regularity Theory for Degenerate PDEs, Bielefeld University. |
| 2017/18 | Introduction to Stochastic Scalar Conservation Laws; Analysis Lecture Series, MPI MiS. |
| 2017 | Introduction to Stochastic Scalar Conservation Laws, Bielefeld University; Variational Approach to SPDEs, MPI MiS. |
| 2016/17 | Introduction to Stochastic Partial Differential Equations II, MPI MiS. |
| 2016 | Introduction to Stochastic Partial Differential Equations, MPI MiS. |
| 2015/16 | Probability II, MPI MiS, jointly with Artem Shaposhnikov and Max von Renesse. |
| 2015 | Analysis III, Bielefeld University. |
