Hello, and welcome! I am an assistant professor at the mathematics department of the American University of Beirut. Here is my CV.
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This term (spring 2019), I teach the following course:
In fall 2018, I taught the following courses:
In spring 2018, I taught the following courses:
In fall 2017, I taught the following courses:
- Explicit computation of a Galois representation attached to an eigenform over SL(3) from the H2 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
with values in GL(3,9) attached to an eigenform over a congruence
of SL(3). We obtain in particular a polynomial with Galois group
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 PGL2 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 PGL2(Fℓ) 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
- My PhD thesis, Computing modular Galois representations