I am primarily interested in geometry - from computer graphics to Riemannian manifold embeddings. My main research interests are:
- Computational anatomy: shape analysis for medical imaging and biology.
- Optimal transport theory: generalized sorting algorithms in dimension D > 1.
- Geometric data analysis: graph- and measure-theoretic methods to study large datasets.
July 2020: Geometric data analyis, beyond convolutions
I defended my PhD thesis on July 2nd, 2020: a related video recording is available here. My thesis is the most comprehensive reference on my work: it is written as an introductory textbook for data sciences and shape analysis, from a geometric perspective. If you just saw one of my talks on symbolic matrices, geometric learning and large-scale optimal transport, here is what you are looking for: KeOps library, GeomLoss package, Slides for the defense, PhD thesis.
I played the flute for 11 years at the Conservatoire Paul Dukas, in Paris. I especially enjoy playing baroque music: J.S. & C.P.E. Bach, J.J. Quantz, G.P. Telemann... In june 2014, I gratuated from the Conservatoire, obtaining a "Certificat de Fin d'Études Musicales" diploma. Here is my leaflet programme, in French: Mathematics in Music.
My other interests include ancient history, Chinese culture and pedagogy. Here are some books that I would strongly recommend:
- Oliver Byrne's "Elements of Euclid": a pedagogical masterpiece.
- Thucydide's history of the Peloponnesian war, a thrilling mix of adventure and reflection.
- Chaos and Dimensions, two movies by Jos Leys, Aurélien Alvarez and Étienne Ghys. A must-see for anyone interested in math!
- Faraday's chemical history of a candle, explained by Bill Hammack, the engineerguy.
- Branch Education's YouTube channel. Clear, concise and illuminating videos on the inner workings of modern hardware.
- Topology from the differentiable viewpoint by John Milnor: a concise and elegant introduction to differential topology. Everything — including Brouwer fixed point theorem and Hopf theorem — is deduced from the single fact that a smooth and compact 1-manifold has an even number of extremal points!
- Hyperbolic geometry by J.W. Cannon: includes a proof of the usual properties of the Poincaré half-plane... without a single calculation, but stereographic projections and symmetries instead.