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
C&O Reading Group - Jacob Skitsko-A Simple Proof of Hardness of Matrix Completion
Abstract: In the matrix completion problem, we are given an incomplete matrix A as input. Some entries are filled in, and some entries have the value "*". Our task is to fill in the "*" entries so that the resulting completed matrix has minimum rank. We'll discuss a simple proof from Shitov showing that it is hard to distinguish between an incomplete matrix having a rank 3 completion, or all completions requiring at least rank 4.
The idea is to index the matrix by vectors. These vectors will represent a circuit computing a family of polynomials, f(x) in F. The hope is that any rank 3 completion will be forced to fill in the matrix values according to these vector labels. Thus, the completion will specify values for x_i, x_j, x_i + x_j, x_i * x_j, ... , and so on until it specifies values for our polynomials f(x). If we force the f(x) in F entries to be 0, then this is exactly a solution to the polynomial system F. Seeing why any rank 3 completion should be forced to operate in this way takes a bit of squinting, but is overall quite pleasant.
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Graphs and Matroids - Lise Turner-Anemones and Matroids of High Branch-Depth
| Speaker: | Lise Turner |
| Affiliation: | University of Waterloo |
| Room: | MC 5479 |
Abstract:We prove a conjecture by DeVos, Kwon and Oum on the unavoidable minors of matroids of high branch-depth. We also consider the properties of collections of crossing low order separations known as anemones. This is joint work with Jim Geelen and Rutger Cambell.
Algebraic and enumerative combinatorics seminar - Hadleigh Frost-Nested nestings, Moment-Cumulant relations and the Combinatorics of the Cosmos
| Speaker: | Hadleigh Frost |
| Affiliation: | Institute for Advanced Study |
| Location: | MC 5417 |
Abstract: Cosmological correlation functions probe the quantum origins of structure in the universe and are a prototype for many calculations in physics. I will share recent work on the complexes, fans and polytopes associated to these functions based on arXiv:2602.21194 and ongoing work. Two structures lie at the heart of this story: (1) incidence relations between chains and anti-chains, (2) a notion of "nested sets of nested sets". Both structures can be studied for an arbitrary lattice, but building sets of the boolean lattice are my main motivation.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.