
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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Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise
Published · Journal de mathématiques pures et appliquées, 148 (2021), pp. 221-266. We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves…
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Regularization and Well-Posedness by Noise for Ordinary and Partial Differential Equations
Published · Stochastic Partial Differential Equations and Related Fields, Springer Proceedings in Mathematics & Statistics 229, pp. 43–67 (2018).
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Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
Published · Probability theory and related fields, 176 (2020) 1/2, pp. 421-448. We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range…
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Entropy solutions for stochastic porous media equations
Published · Journal of differential equations, 266 (2019) 6, pp. 3732-3763. We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well – posedness and $L_1$-contraction is obtained in the class of entropy solutions. Our scope allows…
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Supremum estimates for degenerate, quasilinear stochastic partial differential equations
Published · Annales de l’Institut Henri Poincaré / B : Probabilites et statistiques, 55 (2019) 3, pp. 1765-1796. We prove a priori estimates in $L_\infty$ for a class of quasilinear stochastic partial differential equations. The estimates are obtained independently of the ellipticity constant $arepsilon$ and thus imply analogous estimates for…
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Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise
Published · Archive for rational mechanics and analysis, 233 (2019) 1, pp. 249-322. We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends…
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Density bounds for solutions to differential equations driven by Gaussian rough paths
Published · Journal of theoretical probability, 33 (2020) 2, pp. 611-648. We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution…
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Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
Published · Stochastics and partial differential equations : analysis and computations, 11 (2023) 1, pp. 211-268. The scientific literature contains a number of numerical approximation results for stochastic partial differential equations (SPDEs) with superlinearly growing nonlinearities but, to the best of our knowledge, none of them prove strong…
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Stochastic continuity equations with conservative noise
Published · Journal de mathématiques pures et appliquées, 128 (2019), pp. 225-263. The present article is devoted to well-posedness by noise for the continuity equation. Namely, we consider the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. We prove the…
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Optimal regularity for the porous medium equation
Published · Journal of the European Mathematical Society, 23 (2021) 2, pp. 425-465. We prove optimal regularity for solutions to porous media equations in Sobolev spaces, based on velocity averaging techniques. In particular, the obtained regularity is consistent with the optimal regularity in the linear…
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. |
