- 2021-present: Mihir Deo
- 2020-present: Cédric Dion
- 2017-2021: A Arthur Bonkli Razafindrasoanaivolala (Sur les diviseurs milieux d’un entier , co-supervision with Jean-Marie De Koninck)
- 2016-2020: Jesse Larone (Résolution de certaines équations diophantiennes et propriétés de certains polynômes , co-supervision with Omar Kihel and Claude Levesque )
- 2014-2018: Gautier Ponsinet (On the algebraic side of the Iwasawa theory of some non-ordinary Galois representations )
- 2022-present: Tam Nguyen (PhD student from UBC, co-supervision with R. Sujatha)
- 2021-present: Luochen Zhao (PhD student from John Hopkins)
- 2016: José Ibrahim Villanueva Gutierrez (exchange PhD student from Bordeaux 1)
- 2021-present: Anthony Doyon
- 2019-2021: Fenomila Naivoarilala (Calcul de lambda invariant de la fonction L p-adique d’un caractère de Dirichlet sur un corps quartique)
- 2018-2019: Cédric Dion (Fonction L p-adique d’une forme modulaire )
- 2017-2019: David Ayotte (Relations entre le nombre de classes et les formes modulaires )
- 2022-present: Anwesh Ray (CRM-Simons)
- 2021-present: Katharina Muller
- 2021-present: Jiacheng Xia
- 2020-2021: Jishnu Ray (CRM)
- 2020: Debanjana Kundu (CRM)
- 2018-2020: Antonio Cauchi
- 2017-2019: Guhan Venkat
Undergraduate research projects
- 2022: Sai Sanjeev Balakrishnan, Jeanne Laflamme
- 2021: Anthony Doyon
- 2020: Maxime Cinq-Mars, Anthony Doyon, Antoine Poulin, Michaël Rioux
- 2019: Hugues Bellemare, Anthony Doyon, Sarthak Gupta
- 2018: Hugues Bellemare, Arihant Jain, Antoine Poulin, Mathieu Trudelle
- 2017: Cédric Dion
- 2016: David Ayotte
- 2015: David Ayotte, Jean-Christophe Rondy-Turcotte
Research environment in Ottawa
University of Ottawa is a bilingual university. You can carry out your studies and research in English or in French here. If you study with me, you will be part of the Ottawa-Carleton Number Theory research group, which organizes regular seminars and other academic activities. We are also members of the CRM and the Fields Institute, so you will have the opportunity to participate in many of their activities (seminars, workshops, thematic programmes, etc). Several scholarships are available to Canadian and international students and postdoctoral fellows. More information can be found here.
If you are interested in working with me as a graduate students, you can expect to work on one of the following projets.
1. Factorization of p-adic L-functions
An elliptic curves is a cubic curve that is equipped with a group structure. They are used heavily in modern-day cryptography. In this project you will study the p-adic L-function of an elliptic curve, which is a power series defined over p-adic numbers. It tells us about arithmetic properties of the curve over extensions of the rational numbers that are given by p-power roots of unity. You will investigate how the coefficients of these functions behave. By analysing values of these functions evaluated at a set of special points, you will study whether they factor into functions that are easier to understand. This will result in new arithmetic information on the elliptic curve.
2. Iwasawa theory of modular forms
A modular form is an analytic function that satisfies invariant properties under certain Mobius transforms. In order to prove Fermat’s Last Theorem, Andrew Wiles showed that an elliptic curve is in fact a special case of modular forms. The analytic structure of modular forms allow us to obtain new information about elliptic curves. In this project, you will study certain representations of the Galois group of the rational numbers that are described by the Fourier coefficients of a modular form. More precisely, you will look at the behaviour of these representations as you restrict them to a tower of extensions and understand their cohomology groups.
3. Construction of Euler systems
An Euler system is a family of cohomology classes of a representation that satisfy certain compatibility condition. It is a very powerful tool in Iwasawa Theory because they give us a link between algebraic objects and to analytic objects. In this project, you will study the construction of Euler systems for a certain family of representations and apply them to study asymptotic behaviour of these representations. The construction will rely on understanding the geometry of modular curves and modular surfaces.