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I am an Assistant Professor at the BICMR. Previously, I was a postdoc at Aix-Marseille University in Rémi Rhodes's group, and at HU Berlin in Gaëtan Borot's group. I received my Ph.D. from the University of Cambridge, under the supervision of Jason Miller.
My research deals with conformally invariant stochastic processes, such as Schramm-Loewner evolutions (SLE) and Liouville conformal field theory. I use ideas from harmonic analysis and geometric function theory to connect the probabilistic and algebraic aspects of these processes. Together with Antoine Jego, we used this framework to give a unified approach to three different notions of conformally invariant measures on Jordan curves, answering questions raised by Kontsevich & Suhov. Follow this link for a short account of this work.
Currently, I am using SLE to construct the Belavin-Knizhnik measure in bosonic string theory, addressing an issue pointed out in their landmark 1986 article:
There exist two languages for the description of strings: the algebraic language, making use of representations of infinite dimensional Lie algebras, and the language of sums over surfaces, which leads to the complex-analytic geometry of moduli spaces of Riemann surfaces. A relation between the two approaches does not exist, in the large.
Media
Media
Some of my talks are available online, from compactified to extended version.
Liouville CFT and conformal blocks (3x1h), with Rémi Rhodes
TR, CFT and random geometry
Les Diablerets, (Switzerland). Aug 2025Integration by parts in random conformal geometry (2x1h) [Part I by A. Jego] [Part II]
Probabilistic methods in quantum field theory
Hausdorff Institute for Mathematics, Bonn (Germany). May 2025.SLE loop and CFT(1h).
Random paths to quantum field theory.
SCGP Stony Brook (USA). Oct 2024A probabilistic view on the algebraic structure of Liouville CFT (2x1h) [Notes]
Quantization days 4.0. Online. Dec 2023
Liouville theory: from Segal axioms to conformal blocks (1h).
IPhT Mathematical-Physics seminar.
Saclay (France). Jun 2023.Liouville quantisation of Segal's semigroup (25').
Probability and Mathematical Physics, ICM satellite conference.
Helsinki (Finland). Jul 2022.Singular vectors in Liouville CFT (1h). Uses material from the rest of the workshop
Probability in CFT.
EPFL (Switzerland). Apr 2024.
Publications and preprints
Publications and preprints
Coauthors list: Juhan Aru, Alexander Bufetov, Colin Guillarmou, Antoine Jego, Janne Junnila, Antti Kupiainen, Yanqi Qiu, Rémi Rhodes, Vincent Vargas, Mo Dick Wong, Baojun Wu.
The conformal blocks of Liouville CFT.
w/ C. Guillarmou, A. Kupiainen, R. Rhodes. In preparation.Conformal welding and the matter-Liouville-ghost factorisation.
w/ A. Jego. [arXiv]The CFT of SLE loop measures and the Kontsevich-Suhov conjecture.
w/ A. Jego. [arXiv]The semigroup of annuli in Liouville CFT.
w/ C. Guillarmou, A. Kupiainen, R. Rhodes. [arXiv]Noise-like analytic properties of imaginary chaos.
w/ J. Aru, A. Jego, J. Junnila.
Electron. J. Probab. [arXiv] [Journal]Higher equations of motion at level 2 in Liouville CFT.
w/ B. Wu. [arXiv]Irreducibility of Virasoro representations in Liouville CFT.
w/ B. Wu. Ann. Probab. (to appear) [arXiv]The Virasoro structure and scattering matrix for Liouville CFT.
w/ C. Guillarmou, A. Kupiainen, R. Rhodes, V. Vargas.
Probab. Math. Phys. [arXiv] [Journal]On the log-regularity of SLE4. [arXiv]
Fusion asymptotics for Liouville correlation functions.
w/ M. D. Wong.
Ann. Inst. H. Poincaré Probab. Statist. [arXiv] [Journal]A survey of determinantal point processes.
w/ A. I. Bufetov & Y. Qiu.
Adv. Stud. Pure Math. [Journal]Modular bootstrap agrees with the path integral in the large moduli limit.
Electron. J. Probab. [arXiv] [Journal]
My PhD thesis is available here.
Teaching
Teaching
Complex analysis. Summer Semesters 23, 24.
The Gaussian free field: probabilistic and algebraic aspects. Graduate course, Summer Semester 22.
Analysis 1. Winter Semesters 21/22, 22/23, 23/24.
2017 to 2021: Supervisions in Cambridge (probability, measure theory, complex analysis...)
Running
Running
If you can't find me at my desk, I am probably running in the Calanques National Park. Lately, I've developed a taste for trail running and ultra endurance (see my UTMB public page or follow me on Strava). Here is a list of bibs I've worn or plan to wear:
Trail de Cuers (42k, 2200m+). Mar 2025. Race time 5:41.
Trail aux Etoiles by Ceven'trail (63k, 2500m+). Mar 2024. Race time 7:49.
Ut4M 100 Master (98k, 5900m+). Jul 2023. Race time 19:44.
Les Crêtes by Trail Sainte-Victoire (60k, 3000m+). Apr 2023. Race time 9:39.
Tignes Trail (44k, 2800m+). Aug 2021. Race time 6:55.
Ultra-Marin (Trail 58k). Jul 2021. Race time 5:25.
Fitz 5k. Nov 2020. Race time 17'40.
Cambridge half-marathon. Mar 2020. Race time 1:25'09.
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