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- Math 218: Elementary linear algebra with applications (joint with Professors Hazar Abu-Khuzam, Michella Bou Eid, and Sabine El Khoury)
- Math 261: Number theory

- Math 102: Calculus and analytic geometry II (joint with Zadour Khachadourian)
- Math 345: Algebraic number theory

- Math 101: Calculus and analytic geometry I (joint with Professors Florian Bertrand and Giuseppe della Sala)
- Math 261: Number theory

- Explicit computation of a Galois representation attached to an eigenform over SL(3) from the H
^{2}étale of a surface

arXiv preprint, October 2018 (updated January 2019).

We sketch a method to compute mod ℓ Galois representations contained in the H2 étale of surfaces. We apply this method to the case of a representation with values in GL(3,9) attached to an eigenform over a congruence subgroup of SL(3). We obtain in particular a polynomial with Galois group isomorphic to the simple group PSU(3,9) and ramified at 2 and 3 only.

Data are available here. - Hensel-lifting torsion points on Jacobians and Galois representations

arXiv preprint, August 2018.

We show how to compute any Galois representation appearing in the torsion of the Jacobian of a given curve, given the characteristic polynomial of the Frobenius at one prime.

The source code is available here. - Rigorous computation of the endomorphism ring of a Jacobian (joint with Edgar Costa, Jeroen Sijsling, and John Voight)

To appear in Math. Comp.

We describe several improvements to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field. - Modular Galois representation data available for download

These data were computed and certified thanks to the algorithms described in the three articles below. - Companion forms and explicit computation of PGL
_{2}number fields with very little ramification

Published in Journal of Algebra 509.

This article shows how to generalise the algorithms to compute Galois representations attached to modular forms to the case of forms of any level. As an application, we compute representations attached to forms which are supersingular or admit a companion form, and obtain previously unknown number fields of Galois group PGL_{2}(F_{ℓ}) and record-breaking low root discriminants. Finally, we establish a formula to predict the discriminant of such fields. - Certification of modular Galois representations

Published in Math. Comp. 87.

This article presents methods to certify efficiently and rigorously that the output of the algorithms described in the article below is correct. - Computing modular Galois representations

Published in Rendiconti del Circolo Matematico di Palermo, Volume 62, No 3, December 2013.

This article describes how to explicitly compute modular Galois representations associated with a modular newform, and studies the related problem of computing the coefficients of this newform modulo a small prime. - My PhD thesis, Computing modular Galois representations