Page de Gabriel Chênevert
En construction: page Rubik
- Dimension algorithmique et chiffrement post-quantique, intervention plénière au colloque de l'AMQ, Cégep St-Laurent, octobre 2018.
Feb. 23 – March 6, 2015: Visiting Juniata College again
Oct. 21 – Nov. 1, 2013: Invited teacher, Juniata College, Huntingdon PA
- Differential equations: Laplace transforms (mini course)
- Abstract algebra: A group-theoretic introduction to cryptography (mini course)
- Math colloquium talk: A primer of elliptic curves: from Jacobi and Weierstraß to Wiles and Snowden
Monday, March 2, 2015 — online slides
Elliptic curves are probably the mathematical objects that made the headlines most frequently in the last 20 years, yet it might be difficult to grasp precisely what they are, what they do, and why we care so much about them. This talk is an attempt at brushing a very broad, roughly historic, overview of the topic: from very humble beginnings, arising as byproducts of the computation of the perimeter of ellipses; to the rich theory of complex elliptic functions; to their crucial role in Wiles' proof of Fermat's Last Theorem in 1994; to their recent use in modern public-key cryptography (and controversy over a certain pseudo-random number generator).
- Math modeling: Storing data on compact discs (mini-course)
Course material can be found on Moodle
- Number theory: A number-theoretic introduction to cryptography (mini-course)
Sage worksheet that could be viewed with the online Sage server
- Math club talk: A Tale of Many Cubes (including Rubik's)
Wednesday, Oct. 23, 2013 — online slides (Java applets seem to work best with Chrome)
The Rubik's Cube is certainly one of the most popular and iconic puzzles, having captivated generations of enthusiasts for the last 30 years and sold hundreds of millions of units worldwide. One of its features is a staggering number of unique configurations: it would take roughly the current age of the universe to go through them all at the rate of 100 per second.
However, with a bit of ingenuity it is possible to devise ways to solve the puzzle relatively easily (and some are doing it quite fast!); formalizing this will lead us to some interesting algebraic considerations in which other related abstract cubes will be encountered. The (recently settled) problem of the optimal solution will be discussed, as well as some potentially surprising applications to cryptography.
Si vous cherchez quelque chose en particulier, vous le trouverez sans doute ici.
- Les limites de l'intelligence artificielle, AI Contact, mai 2017 [numéro entier]
- (avec B. Parent) Sur la beauté en mathématique, Vues d'ensemble, avril 2016 [détails bonus]
- Representations on the cohomology of smooth projective hypersurfaces with symmetries, Proc. Amer. Math. Soc. 141 (2013), 1185 — 1197 [arXiv]
- The Banach-Tarski paradox, Eureka!, vol. 7 (26), June 2009, pp. 10 — 13 [complete issue]
- Exponential sums, hypersurfaces with many symmetries and Galois representations, Ph.D. thesis, McGill University, 176+xi p., 2008 [A4 version, summary, slides]
- Some remarks on Frobenius and Lefschetz in étale cohomology, Seminar on cohomology, 2004
- (with P. Kassei) Sheaf cohomology, Seminar on cohomology, 2003
- Polynômes de Kazhdan-Lusztig et cohomologie d'intersection des variétés de drapeaux, mémoire de maîtrise, Université de Montréal, 2003
- The Riemann-Hilbert problem, 2002
- Le théorème de Wedderburn, 2001