2024-25
Mathematical Physics and Probability Reading Seminar
Organisers: Roger Tribe and Oleg Zaboronski
The seminar is dedicated to reading papers relevant to our research (first hour) and discussing research problems with our students (second hour). Everyone is welcome to join in for the whole duration or part of the seminar.
Term 1. Tuesdays, 1200-1400, B1.12
Topic: Introduction to the Polchinski equation for interacting particle systems
01/10/24. Organisational meeting
08/10/24, 15/10/24. Roger Tribe, Background on stochastic dynamics (Chapter 2 of [1])
22/10/24, 29/10/24. Oleg Zaboronski, Gaussian integration and the Polchinski equation (Sections 3.1, 3.2 of [1]) Notes 1
05/11/24, 12/11/24, 26/11/24. Oleg Zaboronski, Multi-scale Bakry-Emery criterion (Sections 3.3, 3.5, 6.2, A.2 of [1]) Notes 2
Literature.
[1] Bauerschmidt, R., Bodineau, T. and Dagallier, B., 2023. Stochastic dynamics and the Polchinski equation: an introduction.
arXiv preprint arXiv:2307.07619.
[2] Duch, P., 2024. Construction of Gross-Neveu model using Polchinski flow equation.
arXiv preprint arXiv:2403.18562.
Extra references
[3] On entropy factorisation for weakly-dependent random variables (By Filippo Cesi)
Term 2. Tuesdays, 1200-1400, B3.01 (Week 1), B1.12 (Weeks 2-10)
Meetings with PhD students
Term 3. Tuesdays, 1200-1400, B3.01
Topic: Perturbative renormalisation and the Polchinski equation
29/04/25, 06/05/25. The seminars are cancelled due to speaker's illness
13/05/25. Roger Tribe, Properties of Gaussian measures and the flow equation (Chapters 2.1, 2.2 of [1])
20/05/25. Roger Tribe, Properties of Gaussian measures and the flow equation (Continued)
27/05/25. Roger Tribe, The proof of perturbative renormalisability via the flow equation. (Chapter 2.3 of [1])
03/06/25. Oleg Z, A brief introduction to Berezin integrals (In preparation for reading [3]). NOTES NOTES_II
10/06/25. Oleg Z, Berezin integrals continued; Gross-Neveu I (Section I of [3]) NOTES
17/06/25. Oleg Z, Gross-Neveu-II (Sections I, II of [3])
Literature.
[1] Volkhard F. Muller, 2009.Perturbative Renormalisation by Flow Equations
https://arxiv.org/abs/hep-th/0208211
[2] M. Salmhofer, Renormalisation: An introduction (Springer TMP series)
[3] Duch, P., 2024. Construction of Gross-Neveu model using Polchinski flow equation.
arXiv preprint arXiv:2403.18562.