About Me
I am an assistant professor at the Institute of Mathematics of the Polish Academy of Sciences in Warsaw. Previously, I held postdoctoral positions at the École Polytechnique Fédérale de Lausanne, Adam Mickiewicz University in Poznań, and the Max Planck Institute for Mathematics in the Sciences in Leipzig. I received my PhD in 2017 from the Jagiellonian University in Kraków.
Research interests
My present research focuses on the intersection between probability theory, PDE theory and Euclidean quantum field theory. I am especially interested in problems involving singular stochastic partial differential equations and renormalization. I also have a background in the mathematical aspects of perturbative and axiomatic quantum field theory as well as general relativity.
Recent papers
- P. Duch, M. Gubinelli, Mass gap for the fractional \( \Phi^4_2 \) model, arXiv:2611.17119
- P. Duch, M. Hairer, J. Yi, W. Zhao, Ergodicity of infinite volume \( \Phi^4_3 \) at high temperature, arXiv:2508.07776
- P. Duch, Construction of Gross-Neveu model using Polchinski flow equation, arXiv:2403.18562
- P. Duch, M. Gubinelli, P. Rinaldi, Parabolic stochastic quantisation of the fractional \( \Phi^4_3 \) model in the full subcritical regime, arXiv:2303.18112
- P. Duch, W. Dybalski, A. Jahandideh, Stochastic quantization of two-dimensional \( P(\Phi) \) Quantum Field Theory, arXiv:2311.04137
- P. Duch, Renormalization of singular elliptic stochastic PDEs using flow equation, arXiv:2201.05031
- P. Duch, Flow equation approach to singular stochastic PDEs, arXiv:2109.11380
For a complete list of published papers and preprints see my arXiv or Google Scholar profiles.
Lecture notes
Lecture notes for the course "Singular stochastic PDEs" taught at SISSA (Trieste, 9-20 March 2026).
Lecture notes for the course "Theory of stochastic calculus" taught at EPFL (Lausanne, Spring 2025).
Lecture notes for the mini-course "Flow equation approach to singular stochastic PDEs" taught at "Summer School on Stochastic Analysis" (Lausanne, 7-18 August 2023) and at "Sino-German Conference on Stochastic Analysis" (Beijing, 16-27 September 2024).
Lecture notes for the mini-course "Construction of fractional \( \Phi^4_3 \) model of Euclidean QFT using flow equation approach to singular SPDEs" taught at the workshop "New developments and challenges in Stochastic Partial Differential Equations" (Lausanne, 17-21 June 2024).
Organisation
47th LQP workshop "Foundations and Constructive Aspects of QFT" (21-22 September 2023, co-organiser).
Contact
Email: pduch at impan dot pl
Institute of Mathematics
Polish Academy of Sciences
Śniadeckich 8
00-656 Warsaw
Poland
Office: 220