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 and enumerative combinatorics seminar-Taylor Brysiewicz
Title: The degrees of Stiefel Manifolds
| Speaker | Taylor Brysiewicz |
| Affiliation | Western |
| Location | MC 6029 |
Abstract:
The set of orthonormal bases for k-planes in R^n is cut out by the equations X*X^T = I
where X is a k x n matrix of variables and I is k x k identity. This space, known as the Stiefel manifold St(k,n), generalizes the orthogonal group and can be realized as the homogeneous space O(n)/O(n-k). Its algebraic closure
gives a complex affine variety, and thus, it has a degree.
I will discuss our derivation of these degrees. Extending 2017 work on the degrees of special orthogonal groups, joint work with Fulvio Gesmundo gives a combinatorial formula in terms of non-intersecting lattice paths.
This result relies on representation theory, commutative algebra, Ehrhart theory, polyhedral geometry, and enumerative combinatorics.
I will conclude with some open problems inspired by these objects.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.
Algebraic Graph Theory-Sarah Bockting-Conrad-Tridiagonal pairs of Racah type and their associated objects
| Speaker: | Sarah Bockting-Conrad |
| Affiliation: |
DePaul University |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: In this talk, we consider a linear algebraic object known as a tridiagonal pair which arises naturally in the context of Q-polynomial distance-regular graphs. We will focus on a special class of tridiagonal pairs said to have Racah type. Given a tridiagonal pair of Racah type, we associate with it several linear transformations which act on the underlying vector space in an attractive manner and discuss their relationships with one another. In an earlier work, we introduced the double lowering operator Ψ for a tridiagonal pair. In this talk, we will explore this double lowering map further under the assumption that our tridiagonal pair has Racah type and will use the double lowering map to obtain new relations involving the operators associated with two oriented versions of our tridiagonal pair.