I am currently a member in mathematics at the Institute for Advanced Study. Previously I was an NSF post-doc in the mathematics department of Columbia University.
I obtained my PhD in 2018 from École Normale Supérieure in Paris, working under the supervision of Rémi Rhodes and Vincent Vargas.
My interests lie at the interface between probability theory, mathematical physics, and geometry. In particular I am currently studying the Liouville conformal field theory. This field theory allows us to understand random geometry in two-dimensions: it has strong links with many canonical two-dimensional random objects such as the Gaussian free field, Gaussian multiplicative chaos, Schramm-Loewner evolutions, and random planar maps. Liouville theory is also a conformal field theory (CFT) which means it is integrable and we can use the framework of CFT developed by Belavin, Polyakov, and Zamolodchikov (1984) to perform many explicit computations.
Link to a short talk given at IAS summarizing my research interests: video.
Articles
Publications in probability and mathematical physics
Analyticity and symmetry of Virasoro conformal blocks via Liouville CFT (with P. Ghosal, X. Sun, and Y. Sun), in preparation, PDF.
Probabilistic derivation of higher equations of motion in Liouville CFT (with K. Aleshkin), in preparation, PDF.
Proof of the Ponsot-Teschner formula for boundary Liouville CFT (with M. Ang, X. Sun, and T. Zhu), in preparation, PDF.
The moduli of annuli in random conformal geometry (with M. Ang and X. Sun), paper submitted to Journal of the AMS, arXiv:2203.12398.
FZZ formula of boundary Liouville CFT via conformal welding (with M. Ang and X. Sun), Journal of the European Mathematical Society, arXiv:2104.09478.
Probabilistic conformal blocks for Liouville CFT on the torus (with P. Ghosal, X. Sun, and Y. Sun), paper under revision at Duke Mathematical Journal, arXiv:2003.03802.
Integrability of boundary Liouville conformal field theory (with T. Zhu), Communications in Mathematical Physics, arXiv:2002.05625.
Liouville quantum gravity with central charge in (1,25): a probabilistic approach (with E. Gwynne, N. Holden, and J. Pfeffer), Communications in Mathematical Physics, arXiv:1903.09111.
The distribution of Gaussian multiplicative chaos on the unit interval (with T. Zhu), Annals of Probability, arXiv:1804.02942.
Liouville quantum gravity on the annulus, Journal of Mathematical Physics, arXiv:1711.06547.
The Fyodorov-Bouchaud formula and Liouville conformal field theory, Duke Mathematical Journal, arxiv:1710.06897.
