Publications

2017
Supporting Diversity in Mathematics Departments
Bélanger-Rioux R. Supporting Diversity in Mathematics Departments. SIAM News [Internet]. 2017;January/February 2017. Publisher's VersionAbstract

Most mathematics departments are not very diverse. Many mathematical sciences and mathematics education faculty would like this to change, but feel lost as to what they can do as individuals. This challenge motivated me to organize “Increasing Diversity and Inclusion in Mathematics: Some Inspiring Initiatives,” a minisymposium at the inaugural SIAM Conference on Applied Mathematics Education (ED16) last September.

2015
Demanet L, Bélanger-Rioux R. Compressed absorbing boundary conditions via matrix probing. SIAM Journal on Numerical Analysis [Internet]. 2015;53 (5) :2441–2471. PreprintAbstract

Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an Absorbing Boundary Condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer stripping elimination of the exterior unknowns, but the linear algebra involved is costly. We propose to bypass the elimination procedure, and directly fit the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. The result is a concise description of the Absorbing Boundary Condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter.

2014
Bélanger-Rioux R. Compressed Absorbing Boundary Conditions for the Helmholtz Equation. Massachusetts Institute Technology [Internet]. 2014. Link to online submitted thesisAbstract

Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer-stripping elimination of the exterior unknowns, but the linear algebra involved is costly. We propose to bypass the elimination procedure, and directly fit the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. We obtain a concise description of the absorbing boundary condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter. We then obtain a fast (nearly linear in the dimension of the matrix) algorithm for the application of the absorbing boundary condition using partitioned low rank matrices. The result, modulo a precomputation, is a fast and memory-efficient compression scheme of an absorbing boundary condition for the Helmholtz equation.

2010
Bélanger-Rioux R. De l'Ordre au Désordre (From Order to Disorder). Accromath [Internet]. 2010;5 (1). Publisher's VersionAbstract

Article based on my high school senior thesis in a French language magazine aimed at engaging high school students and teachers to explore mathematics.

The subject is tilings of the plane, especially aperiodic tilings and their relationship with the Fibonacci numbers and the Golden Ratio.

2007
Bélanger-Rioux R, Filip I. Spectrum and Expansion of Biregular Graphs. Delta Epsilon, the McGill Undergraduate Mathematics Journal [Internet]. 2007;(2) :26-29. Publisher's VersionAbstract

Graphs with a strong expansion property are extremely useful in many areas of mathematics and computer science, particularly in the design of efficient algorithms. It is, however, very difficult to explicitly construct infinite families of good expanders. In this paper, we study the spectrum of biregular graphs and show how it is related to their expansion coefficient. We also describe a construction of biregular expanders from elliptic curves. Finally, we present some experimental results on the second largest eigenvalues of biregular graphs with degrees 2 and 7.