Benjamin Gess

Portrait of Benjamin Gess
Photo: Universität Bielefeld / Michael Adamski

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

Personal academic website
MPI MiS profile

Curriculum vitae

DateAppointment / education
2024–presentW3 Professor, Technische Universität Berlin.
2021–presentResearch group leader, Stochastic Analysis in the Sciences, Max Planck Institute for Mathematics in the Sciences.
2019–2024W3 Professor, Bielefeld University.
2016–2021Max Planck research group leader, Max Planck Institute for Mathematics in the Sciences.
2013–2015Postdoctoral researcher, University of Chicago, supported by a DFG research fellowship.
2012–2013Postdoctoral appointments at TU Berlin, Humboldt-Universität zu Berlin and Bielefeld University.
2009–2011PhD in Mathematics, Bielefeld University; advisor: Michael Röckner; summa cum laude.
2007–2008MSc in Mathematics, University of Warwick; with distinction.
2004–2007Studies 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.

  • Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift

    Published · Inventiones mathematicae, 234 (2023) 2, pp. 573-636. Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…

  • Synchronisation by noise for the stochastic quantisation equation in dimensions 2 and 3

    Published · Stochastics and Dynamics 20(6), 2040006 (2020). We prove uniform synchronisation by noise with rates for the stochastic quantisation equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the…

  • Random attractors for locally monotone stochastic partial differential equations

    Published · Journal of differential equations, 269 (2020) 4, pp. 3414-3455. We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive Lévy noise. The main result is applicable…

  • Ergodicity for Stochastic Porous Media Equations

    Published · SIAM journal on mathematical analysis, 52 (2020) 5, pp. 4524-4564. The long time behaviour of solutions to stochastic porous media equations on smooth bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates the existence and uniqueness of invariant measures…

  • The stochastic thin-film equation: existence of nonnegative martingale solutions

    Published · Stochastic processes and their applications, 130 (2020) 12, pp. 7260-7302. We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise in one space dimension and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter-Kato-type decomposition…

  • Stochastic nonlinear Fokker-Planck equations

    Published · Nonlinear analysis / A, 187 (2019), pp. 259-278. The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting…

  • Convergence rates for the stochastic gradient descent method for non-convex objective functions

    Published · Journal of machine learning research, 21 (2020) 136, pp. 1-48. We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions…

  • Optimal regularity in time and space for the porous medium equation

    Published · Analysis and PDE, 13 (2020) 8, pp. 2441-2480. Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is…

  • Nonlinear diffusion equations with nonlinear gradient noise

    Published · Electronic journal of probability, 25 (2020), p. 35. We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the…

  • Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

    Published · BIT : numerical mathematics, 60 (2020) 4, pp. 1057-1073. Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particular, we establish the optimality of strong convergence…

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.

DateTalk or event
2026FOCM, Vienna — Thermodynamically Consistent and Positivity Preserving Discretization of the Stochastic Thin Film Equation.
202615th AIMS Conference, Athens — Large Deviations for the Porous Medium Equation via Multiscale Integrability.
2026Sorbonne Université, conference celebrating Felix Otto — Gradient-flow structures for porous-media equations, large deviations and multiscale analysis.
2026STOCHASTICA SNIP seminar — Large Spikes in SGD: A Large-Deviations View of Catapults.
2026SIAM 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.
2026MFO, Flows on Measure Spaces and Applications in Machine Learning — Effective fluctuating continuum models for stochastic gradient descent.
2026MFO, Modern and Emerging Phenomena in Machine Learning — Large Spikes in SGD: A Large-Deviations View of Catapults.
2026CoScaRa Annual Meeting, MPI MiS — Rough and nonlinear transport in stochastic fluid dynamics.
2025Mathematics Colloquium, University of Freiburg — Fluctuations in continuum.
2025Mathematics Colloquium, University of Augsburg — Fluctuations in continuum.
2025Beijing–Hong Kong PDE Seminar — From large deviations around porous media to PDEs with irregular coefficients and gradient-flow structures.
2025Workshop on Geometry, Topology, and Machine Learning, MPI MiS — Fluctuating continuum models for stochastic gradient descent on curved spaces.
2025MFO, Probabilistic Perspectives in Neural Network-Based Machine Learning — Effective fluctuating continuum models for Riemannian stochastic gradient descent.
2025TU Berlin semester opening — Fluctuations in continuum.
2025MPI MiS CRC Day — Fluctuations and stochastic dynamics in singular and interacting systems.
2025Langenbach Seminar, WIAS — From large deviations around porous media to PDEs with irregular coefficients and gradient-flow structures.
20258th International Conference on Random Dynamical Systems, Konstanz — Effective fluctuating continuum models for stochastic gradient descent.
2025SPP 2410 workshop, Clausthal — Path-by-path regularization by noise for scalar conservation laws.
2025Conservation Laws and Non-reciprocity, Münster — Gradient-flow structures and large deviations for porous-media equations.
2025École normale supérieure, Paris — Gradient-flow structures and large deviations for porous-media equations.
2025Bielefeld University Uncertainty Colloquium — Taming uncertainty and profiting from randomness in machine learning.
202560th Netherlands Mathematical Congress, plenary lecture — Fluctuations in continuum.
2025TRR 388 opening conference, Berlin — Gradient-flow structures and large deviations for porous-media equations.
2025Stochastic Equations and Particle Systems, Sapienza University of Rome — Gradient-flow structures and large deviations for porous-media equations.
2025GPSD, Dresden — Effective fluctuating continuum models for SGD with small learning rate or in overparameterized limits.
2025GPSD, Dresden — Landau–Lifshitz–Navier–Stokes equations: large deviations and the energy equality.
2025Academy of Sciences and Literature — Fluctuations in continuum.
2025ESI Vienna — Optimal regularity for the nonlocal anisotropic porous-medium equation.
2024Cortona — Effective fluctuating continuum models for SGD with small learning rate or in overparameterized limits.
2024EPFL Lausanne — Large deviations from porous media, gradient-flow structures and SPDEs.
2024ETH Zurich, Modern Perspectives in Applied Mathematics — From large deviations around porous media to PDEs with irregular coefficients and gradient-flow structures.
2024TU Delft, SPDEs Below Sea Level — Large deviations from porous media, gradient-flow structures and SPDEs.
2024NorPDE, Oslo — Optimal regularity for the nonlocal anisotropic porous-medium equation.
2024Hamburg Colloquium on Mathematical Statistics and Stochastic Processes — Large deviations from porous media and gradient-flow structures.
2024Seoul National University Probability Seminar — Large deviations from porous media and gradient-flow structures.
2024Imperial College London — Large deviations from porous media and gradient-flow structures.
2024ESI Vienna — Large deviations from porous media and gradient-flow structures.
2024CIRM Marseille — Large deviations from porous media and gradient-flow structures.

Teaching

TermCourse or seminar
Summer 2026Seminar: Mathematics of Machine Learning; Seminar: Stochastic Analysis in the Sciences.
Winter 2025/26Seminar: Mathematics of Machine Learning; Seminar: Stochastic Analysis in the Sciences.
Summer 2025Seminar: Mathematics of Machine Learning; Seminar: Stochastic Analysis in the Sciences.
Winter 2024/25Seminar: Mathematics of Machine Learning.
Winter 2023/24Seminar: Mathematics of Machine Learning.
Summer 2023Seminar: Mathematics of Machine Learning.
Winter 2022/23Analysis I; Mathematics of Machine Learning; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar.
Summer 2022Mathematics for Natural Sciences II; Mathematics of Machine Learning III; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar.
Winter 2021/22Analysis II; Mathematics of Machine Learning II; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar.
Summer 2021Analysis I; Mathematics of Machine Learning; Stochastic Analysis in the Sciences cluster group; Stochastic Afternoon seminar.
Winter 2020/21IRTG lecture: Large Deviation Estimates; Selected Topics in Large Deviations Theory; Stochastic Analysis research group.
2020Large Deviations II.
2019/20Large Deviations for Stochastic PDE I; Stochastic Thin-Film Equations at MPI MiS and Bielefeld University.
2019Introduction to Singular SPDEs and Stochastic Variational Inequalities, MPI MiS; Stochastic Variational Inequalities, Bielefeld University.
2018/19Random Dynamical Systems and Stochastic Porous-Media Equations with Nonlinear Noise, MPI MiS and Bielefeld University.
2018Optimal Regularity Theory for the Porous-Medium Equation, MPI MiS; Regularity Theory for Degenerate PDEs, Bielefeld University.
2017/18Introduction to Stochastic Scalar Conservation Laws; Analysis Lecture Series, MPI MiS.
2017Introduction to Stochastic Scalar Conservation Laws, Bielefeld University; Variational Approach to SPDEs, MPI MiS.
2016/17Introduction to Stochastic Partial Differential Equations II, MPI MiS.
2016Introduction to Stochastic Partial Differential Equations, MPI MiS.
2015/16Probability II, MPI MiS, jointly with Artem Shaposhnikov and Max von Renesse.
2015Analysis III, Bielefeld University.