Regularity Structures Winter Term 2026/27
Overview
This reading group is an introduction to Martin Hairer鈥檚 theory of regularity structures. It is aimed at people with little to no experience with stochastic PDEs, so no prior knowledge of singular SPDEs is assumed.
We will be closely following these lecture notes by Ajay Chandra and Hendrik Weber:
The first session will take place on Wednesday 7 October, 14:00–15:00, in Zeeman A1.01. We will then meet every Wednesday at the same time and place throughout Terms 1 and 2.
If you have any questions please email Haokai Xie or Theodoros Galanis.
Notes
We are brewing a set of notes based on the presentations given in the reading group, which are available under this . After each session we will try to expand them with the material covered by the speaker.
Mailing List
Starting from Week 4 of this term, we will use a mailing list to communicate with people participating in the reading group. We've created a where you can leave a note with your preferred email address so that we can add you to the list.
Schedule
The following is a rough schedule for the reading group.
| Session | Speaker | Topic | Corresponding sections of the notes |
|---|---|---|---|
| 1 | Theodoros Galanis | Overview: the equations, white noise, scaling, and why renormalisation is needed | 搂1, 搂1.1, 搂1.2 |
| 2 | Haokai Xie | Parabolic H枚lder–Besov spaces and a Kolmogorov theorem | 搂2.1 |
| 3 | JP | Linear theory: Duhamel鈥檚 formula, Schauder estimates and the graphical notation | 搂2.2 |
| 4 | TBC | Nonlinear equations in d = 1, and a primer on iterated integrals | 搂2.3 (up to 搂2.3.1), Appendix A |
| 5 | TBC | Wick powers and the renormalised Picard iteration | 搂2.3.1, 搂2.3.2 |
| 6 | TBC | The Da Prato–Debussche argument and its breakdown in d = 3 | 搂3.1 |
| 7 | TBC | Stochastic renormalisation of the 桅43 trees | 搂4.1 (first part), 搂4.2 (first part) |
| 8 | TBC | The abstract framework: regularity structures, models and modelled distributions | 搂3.2, 搂3.3, 搂3.4 |
| 9 | TBC | Regularity structures for SPDEs: symbols, rules, and the 桅42 and 桅43 structures | 搂3.6, 搂3.7, 搂3.8 |
| 10 | TBC | Canonical and renormalised models | 搂4.1, 搂4.2 |
| 11 | TBC | Reconstruction and multiplication | 搂4.3 |
| 12 | TBC | Integration | 搂4.4 |
| 13 | TBC | The fixed point argument, and wrap-up | 搂4.5 |