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
Tutte colloquium-Ahmad Abdi
Title:Strongly connected orientations and integer lattices
| Speaker: | Ahmad Abdi |
| Affiliation: | London School of Economics and Political Science |
| Location: | MC 5501 |
Abstract: Let D = (V, A) be a digraph whose underlying graph is 2-edge-connected, and let P be the polytope whose vertices are the incidence vectors of arc sets whose reversal makes D strongly connected. We study the lattice theoretic properties of the integer points contained in a proper 'slanted' face F of P. We prove under a mild necessary condition that the 0,1 points in F contain an integral basis B, i.e., B is linearly independent, and every integral vector in the linear of span of F is an integral linear combination of B. This result is surprising as the integer points in F do not necessarily form a Hilbert basis.
Our result has consequences for head-disjoint strong orientations in hypergraphs, and also to a famous conjecture by Woodall that the minimum size of a dicut of D, say k, is equal to the maximum number of disjoint dijoins. We prove a relaxation of this conjecture, by finding for any odd prime number p, a p-adic packing of dijoins of value k and of support size at most 2|A|. We also prove that the all-ones vector belongs to the lattice generated by the 0,1 points in F, where F is the face of P satisfying x(C) = 1 for every minimum dicut C.
This is based on joint work with Gerard Cornuejols, Siyue Liu, and Olha Silina.
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)