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
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.
Sina Kalantarzadeh 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.
Two 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 -Mike Cummings-Webs and smooth components of two column Springer fibers
| Speaker: | Mike Cummings |
| Affiliation: | University of Waterloo |
| Location: | MC 6460 |
Abstract: When you encounter an algebraic variety in the wild, you might ask: What do its components look like? Which components are smooth? How do the components intersect? For Springer fibres, answers to these questions are only known in some very special cases. This is particularly surprising because other aspects Springer fibres have been studied for the past 50 years and they appear throughout combinatorics and adjacent areas. For just one example: Hall–Littlewood polynomials can be obtained from the cohomology of Springer fibres by taking graded Frobenius characteristic.
One classical theorem says that the components of Springer fibers are indexed by standard Young tableaux. In this talk, we will discuss the benefits of instead using webs to index the components in two cases: the "two row" case, and our recent contributions in the "two column" case. We will see that in these cases, webs both characterize and describe the smooth components of Springer fibres, and give a geometric interpretation of rotation of webs.
There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.
Crypto Reading Group - Bruce Xu and Maggie Simmons-HQC Implementation and Optimisation
Abstract: This week will cover the implementation and optimization of key sub-routines within HQC. We will begin by examining the implementation of Reed-Solomon decoding within HQC, which includes the BCH-view of syndromes, weighted Newton's identity, the Berlekamp-Massey algorithm, and more. We will also discuss high-performance polynomial multiplication via the Karatsuba algorithm and hardware optimization.
References: [3] and [4]
[3] J. Dong, Y. Hou, S. Wang, L. Sha, F. Xiao, Z. Dong, and J. Lin. HIGH: Harnessing GPU Parallelism for Optimized HQC Performance. In IACR Cryptology ePrint Archive, 2026.
[4] HQC Team. Hamming Quasi-Cyclic (HQC), NIST Submission, 2025.
A week-by-week plan is outlined at the following link: https://www.leonardocolo.com/seminars/Spring26.html.
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CombOpt ReadingGroup - Rian Neogi-Multidimensional Budget-feasible mechanism design
Abstract: In budget-feasible mechanism design, there is a set of items U. A buyer wishes to purchase a set of items from the sellers of maximum value, where the value of a subset S of items is provided by a valuation function v. Each element e is held by a distinct seller, who incurs a private cost c_e for supplying her item. The buyer also has a budget of B on the total payments made to the sellers. The private costs c_e are known only to the sellers, and not to the buyer. Each seller e reports a cost r_e to the mechanism, which may or may not be equal to her true cost c_e. As a result, a seller may choose to misreport her cost if she sees that she is better off when doing so (for example, the mechanism might be giving her a higher payment under the misreported cost).
Budget-feasible mechanisms have been well-studied over the past 15 years. In this talk, we will introduce a generalization of the setting, where each agent can now hold multiple items. This generalizes the problem into what is known as a multi-parameter domain, which brings about several complications, including strong impossibility results with respect to the typical benchmark of the algorithmic optimum. In lieu of these impossibility results, we propose a novel benchmark for the setting. We prove positive results with respect to this new benchmark, qualitatively matching prior results in single-parameter budget-feasible mechanism design.
This is joint work with Kanstantsin Pashkovich and Chaitanya Swamy, and is to appear in EC 2026.
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