Publications
See also a list of talks that covered some of these.
Machine learning
I led or co-led the following reports at Daedalean:
- Concepts of Design Assurance for Neural Networks
Daedalean and the European Union Aviation Safety. March 2020. 104 pages. - Concepts of Design Assurance for Neural Networks II
Daedalean and the European Union Aviation Safety. May 2021. 113 pages. - Neural Network Based Runway Landing Guidance for General Aviation Autoland
Daedalean. Federal Aviation Administration (William J. Hughes Technical Center, Aviation Research Division). November 2021. 140 pages.
Math
Papers
In chronological order of writing (rather than publication). The links on the title lead to the publisher (most often with a paywall); the PDF might differ slightly from the published versions.
- Gaussian distribution of short sums of trace functions over finite fields
Mathematical Proceedings of the Cambridge Philosophical Society 163(3)
November 2017. 42 pages. PDF - Integral monodromy groups of Kloosterman sheaves
Mathematika 64(3)
June 2018. 27 pages. PDF - Distribution questions for trace functions with values in cyclotomic integers and their reductions
Transactions of the AMS 371(7)
April 2019. 48 pages. PDF - Exponential sums and the large sieve
International Mathematics Research Notices
August 2018. 28 pages. PDF - Joint distribution of inverses in matrix groups over finite fields
Research in Number Theory 5(4)
November 2019. 16 pages. PDF - The average number of subgroups of elliptic curves over finite fields
Quarterly Journal of Mathematics 71(3)
July 2020. 39 pages. PDF - A note on the dimension of the largest simple Hecke submodule
with Sandro Bettin and Maksym Radziwiłł
International Mathematics Research Notices
December 2018. 11 pages. PDF - Roots of $L$-functions of characters over function fields, generic linear independence and biases
Algebra & Number Theory
2020. 41 pages. PDF
Survey
Some recent interactions of probability and number theoryNewsletter of the European Mathematical Society
March 2019. 8 pages.
Thesis
Probabilistic aspects of short sums of trace functions over finite fieldsETH Zürich. 2016 (updated version, 2017). 170 pages.
Student projects
By the nature of these documents, no claim of originality or correctness.- Associating abelian varieties to weight-2 modular forms: the Eichler-Shimura construction
Master thesis (Stanford/EPFL), 2014. 111 pages. Companion poster - Répartition de Frobenius et application aux courbes elliptiques
EPFL. 2013. 100 pages. - The correspondence between binary quadratic forms and quadratic fields
EPFL. 2012. 99 pages.