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 and enumerative combinatorics seminar-Karen Yeats
Tubings of rooted trees and resurgence
| Speaker | Karen Yeats |
| Affiliation | University of Waterloo |
| Location | MC 5479 |
Abstract:
I will explain about how tubings of rooted trees can solve Dyson-Schwinger equations and how, when the Mellin transform is a reciprocal of a polynomial with rational roots, then one can extend the notion of, tubings to label the tubes with letters from some alphabets and from there just by standard generatingfunctionology obtain a system of differential equations that is perfectly suited to resurgent analysis.
Joint work with Michael Borinsky and Gerald Dunne, arXiv:2408.15883
There will be NO pre-seminar on September 19.
Tutte colloquium-Bento Natura
A strongly polynomial algorithm for linear programs with at most two non-zero entries per row or column.
| Speaker | Bento Natura |
| Affiliation | Columbia University |
| Location | MC 5501 |
Abstract:We give a strongly polynomial algorithm for minimum cost generalized flow, and hence for optimizing any linear program with at most two non-zero entries per row, or at most two non-zero entries per column. Primal and dual feasibility were shown by Megiddo (SICOMP '83) and Végh (MOR '17) respectively. Our result can be viewed as progress towards understanding whether all linear programs can be solved in strongly polynomial time, also referred to as Smale's 9th problem. Our approach is based on the recent primal-dual interior point method (IPM) due to Allamigeon, Dadush, Loho, Natura and Végh (FOCS '22). The number of iterations needed by the IPM is bounded, up to a polynomial factor in the number of inequalities, by the straight line complexity of the central path. Roughly speaking, this is the minimum number of pieces of any piecewise linear curve that multiplicatively approximates the central path. As our main contribution, we show that the straight line complexity of any minimum cost generalized flow instance is polynomial in the number of arcs and vertices. By applying a reduction of Hochbaum (ORL '04), the same bound applies to any linear program with at most two non-zeros per column or per row. To be able to run the IPM, one requires a suitable initial point. For this purpose, we develop a novel multistage approach, where each stage can be solved in strongly polynomial time given the result of the previous stage. Beyond this, substantial work is needed to ensure that the bit complexity of each iterate remains bounded during the execution of the algorithm. For this purpose, we show that one can maintain a representation of the iterates as a low complexity convex combination of vertices. Our approach is black-box and can be applied to any log-barrier path following method.
Bento Natura is an Assistant Professor in Industrial Engineering and Operations Research (IEOR) at Columbia University. He spent two years as a Postdoctoral Fellow at Georgia Tech, Brown University, and UC Berkeley. Prior to that, he obtained his PhD in Mathematics from the London School of Economics.
His research interests are focused on the areas of algorithms, optimization, and game theory, with a special emphasis on the theory of linear programming.