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 - Kevin Purbhoo- The hook length formula massacree
| Speaker: | Kevin Purbhoo |
| Affiliation: | University of Waterloo |
| Location: | MC 6460 |
Abstract: Around 1900 Young and Frobenius (independently, and through very different techniques) obtained a formula for the dimensions of the irreducible representations of the symmetric group. Some 53 years later, Frame, Robinson and Thrall noticed that the Young-Frobenius formula simplified into the now famous hook length formula. Nowadays there are many proofs, but the hook length formula remains something of a mystery, as if some deeper understanding lies just out of reach. One aspect of this mystery is that none of the proofs seem to indicate how one might come up with the formula in the first place, other than just guessing.
I will attempt to answer that question. It is an improbable tale that meanders through scenes of Young symmetrizers, Schur-Weyl duality, Weyl algebras, elementary combinatorics, and Plücker relations. All because Google's AI gave me a very obviously wrong answer when I was trying to find out the square of a Young symmetrizer.
There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.
Crypto Reading Group - Camryn Steckel-Decoding for Quasi-Cyclic Codes
Abstract: This session focuses on decoding questions specific to quasi-cyclic codes. We will discuss syndrome decoding in the quasi-cyclic setting and compare generic ISD methods with approaches that exploit additional structure. The goal is to better understand the tension between efficiency and security, and to prepare the ground for the study of the HQC scheme.
References: [§6.3, 4], [§3, 6], and [§5, 10]
[4] HQC Team. Hamming Quasi-Cyclic (HQC), NIST Submission, 2025.
[6] C. Löndahl, T. Johansson, M. Koochak Shooshtari, M. Ahmadian-Attari, and M. Reza Aref. Squaring attacks on McEliece public-key cryptosystems using quasi-cyclic codes of even dimension. Designs, Codes and Cryptography , vol. 80, pp. 359–377, 2016.
[10] N. Sendrier. Decoding One Out of Many. Post-Quantum Cryptography. PQCrypto 2011. Lecture Notes in Computer Science, vol. 7071, Springer, 2011.
A week-by-week plan is outlined at the following link: https://www.leonardocolo.com/seminars/Spring26.html.
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Tutte Colloquium -Douglas Stebila-Adding functionality to post-quantum cryptography with variants of the Fujisaki-Okamoto transform
| Speaker: | Douglas Stebila |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: The Fujisaki-Okamoto (FO) transform is a fundamental building block in new post-quantum cryptography standards like NIST's ML-KEM, where it is used to convert a weakly secure public key encryption scheme into a key encapsulation mechanism (KEM) secure against active attackers. In this talk, we'll explore two approaches to add extra security and functionality to post-quantum KEMs by enhancing the FO transform. First, we see how a birthday-style collision argument lets an attacker who collects many ciphertexts halve the security of the FrodoKEM and HQC standards, and how extending the FO transform with public salts thwarts this multi-target attack. Second, we turn to implementation flaws: for 19 months, HQC's reference implementation effectively skipped a security-critical verification step, yet basic correctness tests still passed. We show how the principle of "verifiable verification", via an extension of the FO transform, ties security to functionality, so that an implementation which that skips it visibly breaks.