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 - Adrien Segovia-The dimension of semidistributive extremal lattices
| Speaker: | Adrien Segovia |
| Affiliation: | Université du Québec à Montréal |
| Location: | MC 5417 |
Abstract: The order dimension of a partially ordered set (poset), which is often difficult to compute, is a measure of its complexity. Dilworth proved that the dimension of a distributive lattice is the width of its subposet on its join-irreducible elements. We generalize this result by showing that the dimension of a semidistributive extremal lattice is the chromatic number of the complement of its Galois graph (see Section 3.5 of arXiv:2511.18540). We apply this result to prove that the dimension of the lattice of torsion classes of a gentle tree with n vertices is equal to n. No advanced background is required to follow the talk.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm in MC 5417.
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.