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.
Prof. Alfred Menezes is named Fellow of the International Association for Cryptologic Research
The Fellows program, which was established in 2004, is awarded to no more than 0.25% of the IACR’s 3000 members each year and recognizes “outstanding IACR members for technical and professional contributions to cryptologic research.”
C&O student Ava Pun receives Jessie W. H. Zou Memorial Award
She received the award in recognition of her research on simulating virtual training environments for autonomous vehicles, which she conducted at the start-up Waabi.
Events
Algebraic Graph Theory-Sidhanth Mohanty
Title: Explicit Lossless Vertex Expanders
| Speaker: |
Sidhanth Mohanty |
| Affiliation: |
Massachusetts Institute of Technology |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: We give the first construction of explicit constant-degree lossless vertex expanders. Specifically, for any ε>0 and sufficiently large d, we give an explicit construction of an infinite family of d-regular graphs where every small set S of vertices has (1−ε)d|S| neighbors (which implies (1−2ε)d|S| unique-neighbors). Our results also extend naturally to construct biregular bipartite graphs of any constant imbalance, where small sets on each side have strong expansion guarantees. The graphs we construct admit a free group action, and hence realize new families of quantum LDPC codes of Lin and M. Hsieh with a linear time decoding algorithm.
Our construction is based on taking an appropriate product of a constant-sized lossless expander with a base graph constructed from Ramanujan Cayley cubical complexes.
Based on joint work with Jun-Ting Hsieh, Alexander Lubotzky, Assaf Reiner, and Rachel Yun Zhang (https://arxiv.org/abs/2504.15087)
Algebraic and enumerative combinatorics seminar-Alex Fink
Title:The external activity complex of a pair of matroids
| Speaker | Alex Fink |
| Affiliation | Queen Mary University of London |
| Location | MC 5479 |
Abstract: In 2016, Ardila and Boocher were investigating the variety obtained by taking the closure of a linear space within A^n in its compactification (P^1)^n; later work named this the "matroid Schubert variety". Its Gröbner degenerations led them to define, and study the commutative algebra of, the _external activity complex_ of a matroid. If the matroid is on n elements, this is a complex on 2n vertices whose facets encode the external activity of bases.
In recent work with Andy Berget on Speyer's g-invariant, we required a generalisation of the definition of external activity where the input was a pair of matroids on the same ground set. We generalise many of the results of Ardila--Boocher to this setting. Time permitting, I'll also present the tropical intersection theory machinery we use to understand the external activity complex of a pair.
For those who attended my talk at this year's CAAC on this paper, the content of the present talk is meant to be complementary.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,