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 - Jim Geelen-Keeping connectivity under taking minors
| Speaker: | Jim Geelen |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract: Suppose that you are given an ordering of the elements of a $k$-connected matroid, and you want to remove the elements one at a time, in the given order, keeping the intermediate matroids as highly connected as possible. How much connectivity can you keep?
Algebraic and enumerative combinatorics seminar - Jonathan Boretsky-Excluding a line from positroids
| Speaker: | Jonathan Boretsky |
| Affiliation: | McGill University |
| Location: | MC 5417 |
Abstract: For all positive integers l and r, we determine the maximum number of elements of a simple rank-r positroid without the rank-2 uniform matroid U(2, l+2) as a minor, and characterize the matroids with the maximum number of elements. This result continues a long line of research into upper bounds on the number of elements of matroids from various classes that forbid U(2, l+2) as a minor, including works of Kung, of Geelen–Nelson, and of Geelen–Nelson–Walsh. This is the first paper to study positroids in this context, and it suggests methods to study similar problems for other classes of matroids, such as gammoids or base-orderable matroids. This project is based on joint work with Zach Walsh.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.
Crypto Reading Group -Maggie Simmons-Enabling FrodoKEM on Embedded Devices
| Speaker | Maggie Simmons |
| Affiliation | University of Waterloo |
| Location | MC 6029 |
Abstract: FrodoKEM is a lattice-based Key Encapsulation Mechanism (KEM) based on unstructured lattices. From a security point of view this makes it a conservative option to achieve post-quantum security, hence why it is favored over the NIST winners by several European authorities (e.g., German BSI and French ANSSI). Relying on unstructured instead of structured lattices (e.g., CRYSTALS-Kyber) comes at the cost of additional memory usage, which is particularly critical for embedded security applications such as smart cards. For example, prior FrodoKEM-640 implementations (using AES) on Cortex-M4 require more than 80 kB of stack making it impossible to run on embedded systems. In this work, we explore several stack reduction strategies and the resulting time versus memory trade-offs. Concretely, we reduce the stack consumption of FrodoKEM by a factor 2–3× compared to the smallest known implementations with almost no impact on performance. We also present various time-memory trade-offs going as low as 8 kB for all AES parameter sets, and below 4 kB for FrodoKEM-640. By introducing a minor tweak to the FrodoKEM specifications, we additionally reduce the stack consumption down to 8 kB for all the SHAKE versions. As a result, this work enables FrodoKEM on embedded systems.