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
Graphs and Matroids - Agnes Totschnig-Colouring graphs with forbidden 7-vertex minors
| Speaker: | Agnes Totschnig |
| Affiliation: | McGill University |
| Room: | MC 5479 |
Abstract:In 1943, Hadwiger conjectured that every k-chromatic graph has a K_k-minor. While the cases k = 5 and k = 6 have been shown to be equivalent to the Four Colour Theorem, respectively by Wagner, and in seminal work by Robertson, Seymour and Thomas, the cases k at least 7 remain open. We show that any 7-chromatic graph has as a minor the complete graph K_7 with two adjacent edges removed, by extending work of Kawarabayashi and Toft and by proving a new edge-extremal bound. This improves Jakobsen’s result with two arbitrary edges removed. Joint work with Sergey Norin.
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.
Crypto Reading Group - Jack Zhao-Post-Quantum PKE from Unstructured Noisy Linear Algebraic Assumptions: Beyond LWE and Alekhnovich’s LPN
Abstract: Much of post-quantum PKE from unstructured noisy linear algebra relies on LWE or Alekhnovich’s LPN: both assume samples of the form (A, As+e) are computationally indistinguishable from (A, u), but with different noise models. LWE uses “short” errors, while Alekhnovich LPN uses sparse errors. Motivated by uncertainty around future cryptanalytic advances, we ask whether one can still obtain PKE from noisy linear assumptions even if both LWE and Alekhnovich LPN were broken. We talk about two new assumptions: Learning with Two Errors (LW2E), which mixes an LWE-style short error with an LPN-style sparse error, and Learning with Short and Sparse Errors (LWSSE), which uses errors that are simultaneously short and sparse but denser than Alekhnovich LPN. |