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.

Other research interests include large deviations theory, metastability and numerical methods for (S)PDEs.

Publications and Preprints

• 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 ]
  Together with L. Broux and F. Otto.

• Stochastic estimates for the thin-film equation with thermal noise. [ arXiv ]
  Together with R. S. Gvalani.

• 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

Universität Münster
Einsteinstr. 62, 48149 Münster, Germany
Email: markus dot tempelmayr at uni-muenster dot de