Markus Tempelmayr

Welcome

I am currently post-doctoral research associate at TU Wien in the research group of Mate Gerencser. Previously I held post-doc positions at EPFL in the research group of Martin Hairer (funded by a Walter Benjamin fellowship), and at the University of Münster in the research group of Hendrik Weber. I obtained my PhD in 2023 at the Max Planck Institute for Mathematics in the Sciences in Leipzig, supervised by Felix Otto. In 2020 I obtained my Masters degree at TU Wien, where my mentor was Giacomo Di Gesù.

Research

Generally speaking, I'm interested in PDEs arising in physical applications. More precisely, I am interested in situations where randomness comes into play, resulting in (singular) stochastic PDEs which are in need of renormalization. My current focus is on well-posedness and universality of such equations, which sits at the intersection of analysis, probability and algebra.

Publications and Preprints

Weak universality for stochastic reaction-diffusion models with long-range correlated noise. [ arXiv ]
Together with S. Gabriel.
A priori bounds for stochastic porous media equations via regularity structures. [ arXiv ]
Together with H. Weber.
Lecture notes on Malliavin calculus in regularity structures. [ arXiv | doi ]
Together with L. Broux and F. Otto.
Stoch PDE: Anal Comp (2025).
Stochastic estimates for the thin-film equation with thermal noise. [ arXiv | doi ]
Together with R. S. Gvalani.
Commun. Math. Phys. (2026)
Characterizing models in regularity structures: a quasilinear case. [ arXiv | doi ]
Probab. Theory Relat. Fields 192 (2025), 373-429.
Lecture notes on tree-free regularity structures. [ arXiv | doi ]
Together with F. Otto and K. Seong.
Mat. Contemp. 58 (2023), 150-196.
A diagram-free approach to the stochastic estimates in regularity structures. [ arXiv | doi ]
Together with P. Linares, F. Otto and P. Tsatsoulis.
Invent. math. 237 (2024), 1469-1565.
The structure group for quasi-linear equations via universal enveloping algebras. [ arXiv | doi ]
Together with P. Linares and F. Otto.
Comm. Amer. Math. Soc. 3 (2023), 1-64.

Contributions to Proceedings

Convergence of the Two-Dimensional Dynamic Ising-Kac Model to $\Phi^4_2$. [ doi ]
Together with B. Dagallier.
Oberwolfach Report 59 (2023), 3343-3346.
Recentering for rough paths and regularity structures via multi-indices. [ doi ]
Oberwolfach Report 54 (2023), 3073-3076.

Contact

Markus Tempelmayr

TU Wien
Institut für Analysis und Scientific Computing
Wiedner Hauptstraße 8-10
1040 Wien, Austria
Email: markus dot tempelmayr at tuwien dot ac dot at

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