Publications
The catalogue keeps one record per scientific work. A preprint record is updated with journal information rather than duplicated when a journal version appears.
Display scientific works by current members that first became publicly available while the author was a member of SAiS.
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- Benjamin Gess
- Max Sauerbrey
- Adrian Martini
- Paul Nikolaev
- Johannes Müller
- Sarah Geiss
- Dennis Chemnitz
- Javier Castro
- Shanshan Hu
- Thomas Müller
- Tom Hapke
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Mathematical challenges
Publication catalogue
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Stochastic Flows with Strong Shear – Part I: Strong Completeness and Set Attractors
Preprint · 2026-10-05. This work studies strong completeness and set attractors for stochastic flows with strong shear, including how rapid radius-dependent rotation can prevent the existence of a global flow.
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Anomalous properties of 2D active scalars perturbed by rough transport noise
Preprint · 2026-09-22. This work studies regularization, integrability, and dissipation for two-dimensional active scalar equations driven by rough transport noise, including Euler, surface quasi-geostrophic, and incompressible porous media models.
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Parabolic-hyperbolic splitting in support propagation for stochastic porous media equations
Preprint · arXiv:2609.11468 (2026). Max Sauerbrey and Joshua Utley study support propagation and waiting-time phenomena for stochastic porous media equations with conservative noise.
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The Schrödinger equation with fluctuating nonlinearity in the energy space
We study nonlinear Schrödinger equations with nonlinear Stratonovich noise in their energy space $H^1(\mathbb R^d;\mathbb C)$. By combining the stochastic Strichartz estimates derived in [Potential Anal. 41 (2014), pp.\ 269–315] with the approach from [Ann.\ Inst.\ H.\ Poincaré Phys.\ Théor.\…
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Weak synchronisation for McKean–Vlasov SDEs
Synchronisation by noise for McKean–Vlasov stochastic differential equations is investigated. A transfer principle is introduced by which synchronisation by noise and diagonal mixing can be transferred from an associated limiting frozen-diffusion SDE to a genuinely law-dependent McKean–Vlasov SDE. The usefulness…
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Finite speed of propagation and waiting time phenomena for stochastic porous media equations with nonlinear conservative noise
Starting from localized energy estimates, we prove finite speed of propagation for kinetic solutions to stochastic porous media equations with nonlinear conservative noise, the existence and uniqueness of which has recently been established. In particular, we propose a novel iteration technique which…
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The stochastic Cahn-Hilliard equation in critical spaces
We study stochastic Cahn-Hilliard equations in bounded smooth domains with a double-well potential, transport-type noise, and natural Neumann boundary conditions in dimensions $d\le 4$. By employing stochastic maximal regularity techniques and deriving suitable energy estimates, we prove local and global well-posedness. The…
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The Advective Fisher-Rao Geometry of Deterministic Measure Transport
A novel advective Fisher-Rao metric is introduced for optimization tasks on paths of probability measures governed by the continuity equation. This metric is shown to lead to optimal descent directions. It is then shown that this metric arises naturally from three different…
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The stochastic Keller–Segel system in critical spaces
Accepted / forthcoming · Oberwolfach Report for the seminar Stochastic Partial Differential Equations in Critical Spaces. We study stochastic, parabolic-parabolic Keller–Segel equations on the $d$-dimensional torus in scaling critical Besov spaces, for $d \geq 3$. Using stochastic maximal regularity estimates, we prove local well-posedness of the equation, i.e.,…
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Effective fluctuating continuum models for stochastic gradient descent
Workshop report · Oberwolfach Reports 23(1), 821–822 (2026). Fluctuating continuum descriptions of stochastic gradient descent.
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Introduce thermal noise before discretizing, not afterwards!
Workshop report · Oberwolfach Reports 23(1), 803–806 (2026). Incorporating thermal noise before discretising a continuum model.
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Large spikes in SGD: a large-deviations view of catapults
Workshop report · Oberwolfach Reports 23(1), 698–700 (2026). A large-deviations perspective on spikes and catapult behaviour in stochastic gradient descent.