Guillaume Remy

I am currently a member of technical staff at Axiom Math working on building the AI mathematician.

Previously I was a quantitative researcher at Cubist Systematic Strategies, a member in mathematics at the Institute for Advanced Study, and 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.

Email address: remyguillaume9275 at gmail.com

My CV and GitHub.

AI and machine learning research and projects

Statistical benchmarking of transformer models in low signal-to-noise time-series forecasting (with C. Garcia), paper submitted, arXiv:2602.09869, Code.

Math research in probability and mathematical physics

Link to a short talk given at IAS summarizing my math research: video.

My math research lies at the interface between probability theory, mathematical physics, and geometry. In particular I have studied 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.

Analyticity and symmetry of Virasoro conformal blocks via Liouville CFT (with P. Ghosal, X. Sun, and Y. Sun), in preparation, PDF.
Derivation of all structure constants for boundary Liouville CFT (with M. Ang, X. Sun, and T. Zhu), paper submitted, arXiv:2305.18266.
The moduli of annuli in random conformal geometry (with M. Ang and X. Sun), Annals of École Normale Supérieure, 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), 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.

Other publications and writings

Implementing singular value decomposition in zero-knowledge proofs (with A. Marwah and Z. Wu), Code, Blog, Error analysis pdf.
Probabilistic derivation of higher equations of motion in Liouville CFT (with K. Aleshkin), notes.
Integrability of Gaussian multiplicative chaos and Liouville conformal field theory, PhD thesis.
Near-criticality underlies the behavior of early tumor growth (with P. Cluzel), Phys Biol. 2016 Apr 4; 13(2):026005.

Teaching

Accelerated Multivariable Calculus, Columbia University, Fall 2021.
Accelerated Multivariable Calculus, Columbia University, Fall 2020.
Calculus III, Columbia University, Fall 2018.
Probability and Statistics for students of the economics department, École Normale Supérieure in Paris, Fall 2015 - Spring 2018.

Invited talks

May 2023. Probability Workshop, Columbia University.
Apr. 2023. Probability seminar, University of Madison.
Mar. 2023. Lie Groups Quantum Math Seminar, Rutgers University.
Feb. 2023. Physics Group Meeting, IAS.
Feb. 2023. Mathematical Physics Seminar, Princeton University.
Nov. 2022. Oliver Club, Cornell University.
Nov. 2022. Probability seminar, Columbia University.
Oct. 2022. Probability Seminar, MIT.
Sep. 2022. New member short talk, IAS Princeton, video.
Apr. 2022. Probability seminar, EPFL, Lausanne.
Apr. 2022. Probability seminar, Université Paris-Sud.
Dec. 2021. Probability seminar, National University of Singapore.
Dec. 2021. Probability seminar, University of Chicago.
Oct. 2021. Probability seminar, University of Pennsylvania.
Oct. 2021. Online conference on Integrability in Conformal Probability.
May 2021. Columbia-Princeton probability day, online seminar.
Apr. 2021. NYC Integrable Probability Working Group, Columbia University.
Feb. 2021. Probability seminar, City University of New York.
Jan. 2021. Probability seminar, University of Marseille.
Dec. 2020. Random Geometry and Statistical Physics online seminar.
Nov. 2020. Northeast Probability Seminar.
Aug. 2020. Bernoulli-IMS One World Symposium, contributed a short talk.
May. 2020. Random Geometry and Quantum Gravity conference, IHP, Paris.
Mar. 2020. Probability and Mathematical Physics Seminar, Courant Institute, NYU.
Feb. 2020. Probability Seminar, MIT.
Dec. 2019. Probability and Statistics Seminar, Tulane University.
Nov. 2019. Integrable Probability Seminar, Columbia University.
Nov. 2019. Mathematical Physics Seminar, Columbia University.
Nov. 2018. Probability Seminar, City University of New York.
Jul. 2018. Random Geometry Workshop, Cambridge University.
Jun. 2018. Random Conformal Geometry and Related Fields, KIAS, Seoul.
Jun. 2018. Hausdorff School on Log-correlated Fields, Bonn.
Jun. 2018. Probability seminar, Columbia University.
Apr. 2018. Probability seminar, EPFL, Lausanne.
Mar. 2018. Seminar on stochastic processes, ETH Zurich.
Feb. 2018. Les probabilités de demain, IHES, Paris. (slides)