I obtained my PhD in May 2020 from ENS Paris, working under the supervision of Vincent Vargas. There were two main axes in my research work: Gaussian multiplicative chaos (GMC) and Liouville quantum gravity (LQG). GMC is a random measure with density given by the exponential of a log-correlated Gaussian field. It has applications in random matrices, random geometry, statistical physics, finance etc. On the other hand, LQG is a physics theory that lies at the interface of quantum field theory and conformal field theory. My goal is to prove rigorously some conjectures in LQG and deduce as a consequence exact results on GMC.
Publications
- Derivation of all structure constants for boundary Liouville CFT (with Morris Ang, Guillaume Remy, and Xin Sun), arXiv:2305.18266.
- Integrability of boundary Liouville conformal field theory (with Guillaume Remy), arXiv:2002.05625, Communications in Mathematical Physics.
- Higher order BPZ equations for Liouville conformal field theory, arXiv:2001.08476.
- The distribution of Gaussian multiplicative chaos on the unit interval (with Guillaume Remy), arXiv:1804.02942, Annals of Probability.
Teaching
During 2018-2020, I taught statistics for the course "Mathématiques et statistiques pour économistes" at ENS Paris.
- TD1: Probabilités élémentaires.
- TD2: Variables aléatoires.
- TD3: Observations asymptotiques.
- TD complémentaire: Lemme de Borel-Cantelli.
- TD4: Estimations et intervalles de confiance.
- TD5: Tests d'hypothèse.
- Poly du Chap 6: Vecteurs Gaussiens, Note du cours.
- TD6: Vecteurs Gaussien.
- Poly du Chap 7: Tests du Khi 2, Note du cours.
- TD7: Tests du Khi 2.
- Note du Chap 8: Information de Fisher et estimation Bayésienne.
Miscellaneous
- Introduction au domaine de recherche: théorie conforme des champs de Liouville par l'approche probabiliste. [pdf]
- Formule de Benoît-Saint Aubin pour la théorie conforme des champs de Liouville. [pdf]
- Fluctuations de la loi empirique de grandes matrices aléatoires. [pdf], [beamer]
- Théorème de Kaufman. [pdf]
- Transport optimal sous contrainte de type martingale. [pdf]
Activities
- Jun 2019 - Probability and quantum field theory: discrete models, CFT, SLE and constructive aspects, IGESA, Porquerolles, France.
- Jul 2018 - Random geometry follow up, University of Cambridge, UK. (Slides)
- Jun 2018 - Hausdorff school on log-correlated fields, HCM, Bonn, Germany.
- Oct 2017 - Scaling limits of random planar maps and Liouville quantum gravity, MFO, Oberwolfach, Germany.
- Jan 2017 - L'ecole d'hiver combinatoire et interaction, CIRM, Marseilles, France.
- Oct 2016 - 2nd French Russian conference ‘Random geometry and physics’, IHP, Paris, France.
Contact
- Email : tunan.zhu_"shift+2"_ens.fr
- Bureau : V6 / Passage Vert, rez-de-chaussée, escalier B
- Equipe : Probabilités et statistiques
- Etablissement de rattachement : ENS
