Welcome to Combinatorics and Optimization
The C&O department has 33 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
- Graph theory
- Quantum computing
Read more about the department's research to learn of our contributions to the world of mathematics!
The very successful Tutte's 100th Distinguished Lecture Series has now completed. That success has led to a Tutte Distinguished Lecture once per term. The next lecture will happen in the Spring term.
*Recordings of occurred talks are all available on C&O's YouTube Channel.
New Deadline: February 1, '20
- June 11, 2021
Robert Cummings is the recipient of the 2021 Governor General’s Academic Silver Medal for the Faculty of Mathematics. Cummings, an Honours Computer Science and Combinatorics and Optimization student, will graduate this June with a BMath.
- May 21, 2021
"An Invitation to Analytic Combinatorics: From One to Several Variables", written by C&O professor Stephen Melczer, has been published by Springer.
- May 20, 2021
Three Ph.D. and seven M.Math. C&O students will receive their degrees at the Spring 2021 convocation on June 18.
- June 21, 2021
Title: Average Mixing Matrices of Trees and Stars
Speaker: Paula Kimmerling Affiliation: Washington State University Zoom: Contact Soffia Arnadottir
We define the average mixing matrix (AMM) of a continuous-time quantum walk on a graph using the orthogonal projections onto the eigenspaces of the adjacency matrix A. From there, one of the properties that has been studied is the rank of the AMM. This is easiest to do if the eigenvalues of A are simple, and we’ll review some of the results on this from Coutinho et. al. (2018).
- June 24, 2021
Title: Arctic curves for groves
Speaker: Terrence George Affiliation: University of Michigan Zoom: Contact Stephen Melczer
The limit shape phenomenon is a "law of large numbers" for random surfaces: the random surface looks macroscopically like the "average surface". The first result of this kind was the celebrated arctic circle theorem for domino tilings of the aztec diamond. The limit shape has macroscopic regions with different qualitative behavior, and the arctic curve is the boundary separating these regions.
- June 25, 2021
Title: From low probability to high confidence in stochastic convex optimization
Speaker: Dmitriy Drusvyatskiy Affliliation: University of Washington Zoom: Contact Emma Watson
Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either rely on “light-tail” noise assumptions or exhibit worse sample complexity. In this work, we show that a wide class of stochastic optimization algorithms can be augmented with high confidence bounds at an overhead cost that is only logarithmic in the confidence level and polylogarithmic in the condition number.