# Publications

## ML

I led (co-led the first one with David Haber) 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. The links on the title lead to the publisher (most often with a paywall), while PDFs are available by clicking on the icons. These may slightly differ 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. - Integral monodromy groups of Kloosterman sheaves

*Mathematika 64(3)*

June 2018. 27 pages. - Distribution questions for trace functions with values in cyclotomic integers and their reductions

*Transactions of the AMS 371(7)*

April 2019. 48 pages. - Exponential sums and the large sieve

*International Mathematics Research Notices*

August 2018. 28 pages. - Joint distribution of inverses in matrix groups over finite fields

*Research in Number Theory 5(4)*

November 2019. 16 pages. - The average number of subgroups of elliptic curves over finite fields

*Quarterly Journal of Mathematics 71(3)*

July 2020. 39 pages. - 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. - Roots of $L$-functions of characters over function fields, generic linear independence and biases

*Algebra & Number Theory*

2020. 41 pages.

### Survey

Some recent interactions of probability and number theory*Newsletter 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

These are student projects; 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.