The C&O department has 36 faculty members and 60 graduate students. We are intensely research oriented and hold a strong international reputation in each of our six major areas:
- Algebraic combinatorics
- Combinatorial optimization
- Continuous optimization
- Cryptography
- Graph theory
- Quantum computing
Read more about the department's research to learn of our contributions to the world of mathematics!
News
Laura Pierson wins Governor General's Gold Medal
The Governor General’s Gold Medal is one of the highest student honours awarded by the University of Waterloo.
Sepehr Hajebi wins Graduate Research Excellence Award, Mathematics Doctoral Prize, and finalist designation for Governor General's Gold Medal
The Mathematics Doctoral Prizes are given annually to recognize the achievement of graduating doctoral students in the Faculty of Mathematics. The Graduate Research Excellence Awards are given to students who authored or co-authored an outstanding research paper.
Three C&O faculty win Outstanding Performance Awards
The awards are given each year to faculty members across the University of Waterloo who demonstrate excellence in teaching and research.
Events
Algebraic & Enumerative Combinatorics - Santiago Estupiñán
Title: Jeu de Taquin for Mixed Insertion and a Problem of Soojin Cho
| Speaker: | Santiago Estupiñán |
| Affiliation: | University of Waterloo |
| Location: | MC 5417 |
Abstract:
Serrano (2010) introduced the shifted plactic monoid, governing Haiman's (1989) mixed insertion algorithm, as a type B analogue of the classical plactic monoid that connects jeu de taquin of Young tableaux with the Robinson–Schensted–Knuth insertion algorithm. Serrano proposed a corresponding definition of skew shifted plactic Schur functions. Cho (2013) disproved Serrano's conjecture regarding this definition, by showing that the functions do not live in the desired ring and hence cannot provide an algebraic interpretation of tableau rectification or of the corresponding structure coefficients. Cho asked for a new definition with particular properties. We introduce such a definition and prove that it behaves as desired. We also introduce the first jeu de taquin theory that computes mixed insertion. This is joint work with Oliver Pechenik.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm in MC 5417.
Crypto Reading Group - Youcef Mokrani
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Title: Adaptive Attacks Against FESTA Without Input Validation or Constant-Time Implementation
Abstract: A FESTA trapdoor function is an isogeny-based trapdoor function based on an attempt to apply Kani’s theorem to cryptography. This paper claims that there are adaptive attacks for a FESTA-based scheme if this scheme does not check the correctness of the input matrix or is not implemented in constant time. Our attacks do not apply to the constant-time implementation of the IND-CCA PKE scheme named FESTA proposed in the FESTA original paper. In this paper, we provide adaptive attacks for a FESTA trapdoor function using auxiliary oracles, which reveals the secret key of the function. These oracles may be constructed if the FESTA trapdoor function is used without validating the input matrix or implemented in non-constant time. |
Algebraic and enumerative combinatorics seminar - Moriah Elkin- Open quiver loci, CSM classes, and chained generic pipe dreams
| Speaker: | Moriah Elkin |
| Affiliation: | Cornell University |
| Location: | MC 5417 |
Abstract: In the space of type A quiver representations, putting rank conditions on the maps cuts out subvarieties called "open quiver loci." These subvarieties are closed under the group action that changes bases in the vector spaces, so their closures define classes in equivariant cohomology, called "quiver polynomials." Knutson, Miller, and Shimozono found a pipe dream formula to compute these polynomials in 2006. To study the geometry of the open quiver loci themselves, we might instead compute "equivariant Chern-Schwartz-MacPherson classes," which interpolate between cohomology classes and Euler characteristic. I will introduce objects called "chained generic pipe dreams" that allow us to compute these CSM classes combinatorially, and along the way give streamlined formulas for quiver polynomials.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.