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 - Eileen Robinson-Coloring claw-free graphs of bounded codegree
| Speaker: | Eileen Robinson |
| Affiliation: | Université libre de Bruxelles |
| Room: | MC 5479 |
Abstract:We define the codegree of a given graph as the maximum number of neighbors that any two distinct vertices have in common.
Algebraic and enumerative combinatorics seminar-Ashleigh Adams-Promotion, plane partitions, partial evaluations, and webs
| Speaker: | Ashleigh Adams |
| Affiliation: | North Dakota State University |
| Location: | MC 6029 |
Abstract: Webs are graphical objects that give a tangible, combinatorial way to compute and classify tensor invariants. Recently, Gaetz, Pechenik, Pfannerer, Striker, and Swanson (arXiv:2306.12501) found a rotation-invariant web basis for SL₄, as well as its quantum deformation U_q(sl₄), and a bijection between move equivalence classes of SL₄-webs and fluctuating tableaux such that web rotation corresponds to tableau promotion. They also found a bijection between the set of plane partitions in an a×b×c box and a benzene move equivalence class of SL₄-webs by determining the corresponding oscillating tableau. In this talk, I will similarly find the oscillating tableaux corresponding to plane partitions in certain symmetry classes by characterizing them via certain lattice words. A dynamical action on tableaux, called promotion, corresponds to rotation of SL₄-webs. I will show how promotion of certain subtableaux aligns with rotation of their respective webs. I will also show that this correspondence maps through a projection to either SL₂ or SL₃ webs. Moreover, this projection is exactly a partial evaluation of webs. This talk will be given through the lens of the combinatorics of webs and tableaux. Some of this work is joint with Jessica Striker.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.
Algebraic and enumerative combinatorics seminar - Mahrud Sayrafi-Constructing exceptional collections for toric varieties
| Speaker: | Mahrud Sayrafi |
| Affiliation: | McMaster University |
| Location: | MC 5417 |
Abstract: Exceptional collections are a powerful tool for understanding the derived category of coherent sheaves on algebraic varieties, with applications in commutative algebra, birational geometry, and mirror symmetry. While the existence of exceptional collections is known for classical varieties such as Grassmannians and flag varieties, constructing explicit collections for toric varieties presents challenges in combinatorial algebraic geometry. In this talk I will describe a computational approach to constructing full strong exceptional collections consisting of complexes of line bundles for toric varieties. No background in derived categories is assumed.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.