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-Alexander Van Werde
Title: Towards generalized spectral determinacy of random graphs
| Speaker: | Alexander Van Werde |
| Affiliation: | Eindhoven University of Technology |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: Wang and Xu (2006, 2017) discovered sufficient conditions for a graph to be uniquely characterized by the spectra of its adjacency matrix and of its complement graph. They conjectured that these conditions are satisfied with nonvanishing frequency, but this remains open and it was not clear what proof techniques could be used. I will present a new line of attack which approaches the problem as a question about random groups. This allows making connections to proof techniques from combinatorial random matrix theory. The results which I will present are in a toy case, but it is expected that the employed perspective will generalize.
This talk is based on my paper “Cokernel statistics for walk matrices of directed and weighted random graphs” [Combinatorics, Probability and Computing (2025)]
Algebraic and enumerative combinatorics seminar-Leigh Foster
Title:The squish map and the SL_2 double dimer model
| Speaker | Leigh Foster |
| Affiliation | University of Waterloo |
| Location | MC 5479 |
Abstract: A plane partition, whose 3D Young diagram is made of unit cubes, can be approximated by a "coarser” plane partition, made of cubes of side length 2. Two such approximations can be obtained by "rounding up” or "rounding down” to the nearest cube. We relate this coarsening (or downsampling) operation to Young's squish map, introduced in earlier work. We exhibit a related measure-preserving map between the 2-periodic single dimer model on the honeycomb graph, and a particular instance of Kenyon's SL_2 double dimer model on a coarser honeycomb graph. This allows us to apply existing computations from the 2-periodic single dimer partition function to a portion of the parameter space of the the harder double dimer model. We also specialize our map and exhibit new criterion for the signed-tilability of a closed region on the honeycomb graph.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,
Tutte colloquium-Stephan Pfannerer-Mittas
Title:A mystery group action and the mystery statistic
| Speaker: | Stephan Pfannerer-Mittas |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: In 2010, B. Rhoades proved that promotion on rectangular standard Young tableaux together with the associated fake-degree polynomial shifted by an appropriate power, provides an instance of the cyclic sieving phenomenon.
Motivated in part by this result, we show that we can expect a cyclic sieving phenomenon for m-tuples of standard Young tableaux of the same shape and the m-th power of the associated fake-degree polynomial, for fixed m, under mild and easily checked conditions. However, we are unable to exhibit an appropriate group action explicitly.
Put differently, we determine in which cases the mth tensor power of a character of the symmetric group carries a permutation representation of the cyclic group.
To do so, we use a method proposed by N. Amini and P. Alexandersson, which amounts to establishing a bound on the number of border-strip tableaux.
Finally, we apply our results to the invariant theory of tensor powers of the adjoint representation of the general linear group. In particular, we prove the existence of a statistic on permutations, which is equidistributed with the RSK-shape and invariant under rotation.
This is based on joint work with Per Alexandersson, Martin Rubey and Joakim Uhlin.