Teaching

Contents. Lecture series ⋅ Oxford (2022–) ⋅ Bonn (2015–2022) ⋅ Paris Dauphine (2008–2015) ⋅ Paris XI (2006–2008)

Lecture series

• A constructive introduction to quantum field theory – SISSA, 20 October–6 November 2026. Part of the Probability and Stochastic Analysis Trimester Programme.

• Euclidean fields via stochastic analysis – course at the RIMS Spring Workshop “The Mathematical Roads to Quantum Field Theory”, Kyoto, 13–17 April 2026 (url). Lecture notes: The FBSDE approach to stochastic quantisation [PDF].

• A stochastic analysis perspective on Euclidean fields – 53rd Saint-Flour Probability Summer School, 30 June–12 July 2025. Lecture notes and recordings.

• Minicourse in Pavia, June 2025.

• Minicourse at the GSSI Intensive Trimester “Particles, Fluids and Patterns: Analytical and Computational Challenges”, L'Aquila, May 2025 (url).

• SLMath Summer Graduate School “Stochastic quantisation”, Berkeley, July 2024 (url). Organisation and lectures. Lecture notes, based on the Milan course: week 1 [PDF], week 2 [PDF]; notes of the first lecture of week 2, on discrete Besov spaces [PDF].

• Constructive stochastic quantization – CIME summer school “Statistical Mechanics and Stochastic PDEs”, Cetraro, September 2023 (url). Slides: [PDF]. Lecture notes in Statistical Mechanics and Stochastic PDEs: Cetraro, Italy 2023, Lecture Notes in Mathematics 2401, Springer, 2026 (forthcoming).

• Facets of stochastic quantisation – Online Open Probability School (OOPS), September 2021. Recordings: Lecture 1, Lecture 2, Lecture 3. Slides: [1] [2] [3].

• Stochastic quantization of Euclidean quantum field theories – Graduate school of the University of Milan, 15–25 February 2021 (online). Lecture notes and scripts.

• Workshop for students (6 hours) at the Fields Medal Symposium in honour of Martin Hairer, Toronto, 2017.

• Minicourse at the Hausdorff School “Recent Development in Singular Stochastic PDEs”, Bonn, 20–24 February 2017 (url).

• Energy solutions for the stationary KPZ equation – CIME summer school “Singular Random Dynamics”, Cetraro, 22–26 August 2016. Lecture notes in Singular Random Dynamics, Lecture Notes in Mathematics 2253, Springer, 2019.

• Minicourse at the winter school “Recent Breakthroughs in Singular SPDEs”, Milan, 2015. Slides: Lectures on paracontrolled distributions with applications to singular SPDEs [PDF].

• Course at the 18th Escola Brasileira de Probabilidade, Mambucaba, 2014. Lecture notes, with Nicolas Perkowski: Lectures on singular stochastic PDEs, Ensaios Matemáticos 29, Sociedade Brasileira de Matemática, 2015.

• Minicourse at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, 2014.

• Minicourses in Marseille, Berlin and Rome, 2012. Notes of the Berlin minicourse (December 2012): Controlled paths and applications [PDF].

• Lectures on large deviations at the Scuola Normale Superiore, Pisa, 2012. Lecture notes: Notes on large deviations, \(\Gamma\)-convergence and entropy [PDF].

• Minicourse on rough paths, CMLS, École Polytechnique, Palaiseau, 2009.

Past lecture courses and seminars in Oxford (2022–)

• C8.1 Stochastic Differential Equations (MT24) [url]

• Elements of Mathematical Quantum Mechanics – TCC course (TT24) (link)

• C8.1 Stochastic Differential Equations (MT23) [url]

• C8.1 Stochastic Differential Equations (MT22) [url]

Past lecture courses and seminars in Bonn (2015–2022)

• Course: Stochastic Analysis (SS22) (link)

• Master seminar: Rough paths (SS22) (link)

• WS21/22 Sabbatical

• Course: Stochastic Processes (SS21) (link)

• Hauptseminar Stochastik: Statistische Mechanik von Gittersystemen (SS21) (link)

• Master seminar: Nonperturbative renormalization group (WS2021) (link)

• Course: Einfürung in die Wahrscheinlichkeitstheorie (WS2021) (link)

• Course: Functional Integration and Quantum Mechanics (SS20) (link)

• Course: Stochastic Analysis (SS20) (link)

• Bachelor thesis topics (SS20) (pdf)

• Master seminar: The mathematics of Feynman integral (SS20) (link)

• Course: Foundations of Stochastic Analysis (WS1920) (link)

• Bachelor Seminar: Large Deviations (WS1920) (link)

• Course: Stochastic Processes (SS19) (link)

• Bachelor thesis topics (SS19) (pdf)

• Bachelor thesis topics (SS18) (pdf)

• Course: Quantum probability and quantum stochastic calculus (SS18) (link)

• Course: Markov Processes (WS17/18) (link)

• Course: Stochastic Analysis (SS17) (link)

• Course: Rough paths and Controlled paths (WS16/17)

• Summer school: Paraproducts and Analysis of Rough Paths (SS16) (link)

• Course: Stochastic Analysis (SS16) (link)

• Course: Rough paths and Controlled paths (WS15/16) (link)

Past lecture courses and seminars in Paris Dauphine (2008–2015)

Année 2014/2015

• Processus discrets (M1 MMD)

Année 2013/2014

• Processus discrets (M1 MMD)

Année 2012/2013

• Introduction à la theorie des chemins rugueux (M2 EDPMAD,TSI,MASEF)

• Processus discrets (M1 MMD)

• Contrôle des chaînes de Markov (M1 MMD)

Année 2011/2012

• Eléments de mathématiques des décisions collectives (M2 EDPMAD,TSI,MASEF)

• Processus discrets (M1 MMD)

• Contrôle des chaînes de Markov (M1 MMD)

• Processus de Poisson et méthodes actuariels (M1 MMD)

Année 2010/2011

• Analyse des fonctions booléennes (M2 EDPMAD/TSI)

• Processus discrets (M1 MMD)

• Contrôle des chaînes de Markov (M1 MMD)

• Statistique (DU2 Eco IGD Math/Eco Mat/Info)

Année 2009/2010

• Processus discrets (M1 MMD)

• Contrôle des chaînes de Markov (M1 MMD)

• Grandes déviations (M2 EDPMAD/TSI)

• Statistique (DU2 Eco IGD Math/Eco Mat/Info)

Année 2008/2009

• Analyse des EDS (M2 EDPMAD/TSI)

• Contrôle des chaînes de Markov (M1 MMD)

• Statistique (DU2 Eco IGD Math/Eco Mat/Info)

• TD d'Evaluation des actif contingents (M1 MMD)

Past lecture courses and seminars in Paris XI (2006–2008)