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

## Prof. Alfred Menezes is named Fellow of the International Association for Cryptologic Researc

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.

## Jeremy Chiwezer 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.

## Events

## URA Seminar - Stephen Melczer

**Title: **Adventures in Enumeration

Speaker: |
Stephen Melczer |

Affiliation: |
University of Waterloo |

Location: |
MC 5479 |

**Abstract: **We make the argument that by combining pure mathematical tools with computational insights and applications from a vast array of disciplines, combinatorics is the perfect area to see all the wonders of math on display. Applications discussed include the analysis of classical algorithms, restricted permutations, models predicting the shape of biomembranes, queuing theory, random walks, ratchet models for gene expression, maximum likelihood degree in algebraic statistics, transcendence of zeta values, sampling algorithms for perfect matchings in bipartite graphs, and parallel synthesis for DNA storage.

## Graphs and Matroids - Massimo Vicenzo

**Title: **Reconstructing Shredded Random Matrices

Speaker: |
Massimo Vicenzo |

Affiliation: |
University of Waterloo |

Location: |
MC 5479 |

**Abstract: **The Graph Reconstruction Conjecture states that if we are given the set of vertex-deleted subgraphs of some graph, then there is a unique graph G that can be reconstructed from them. This conjecture has been open since the 60s, and has only been solved for certain classes of graphs with not much progress towards the general case. We instead study adjacent reconstruction problems, for example, studying matrices instead of graphs: Given some binary matrix M, suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, are we able to recover the original matrix and will it be unique? We present an algorithm that identifies whether there is a unique ordering associated with a set of rows and columns, and outputs either the unique correct orderings for the rows and columns or the full collection of all valid orderings and valid matrices. We show that for matrices with entries that are i.i.d. Bernoulli(p), that for p >2log(n)/n that the matrix is indeed unique with high probability. This is a joint work with Caelan Atamanchuk and Luc Devroye.

## Algebraic and Enumerative Combinatorics - Li Yu

**Title: **Integrable systems on the dual space of Lie algebras arising from log-canonical cluster structures

Speaker: |
Li Yu |

Affiliation: |
University of Toronto |

Location: |
MC 6029 |

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.

**Abstract: **Let $(X, \{~,~\})$ be an (affine) Poisson variety. A log-canonical cluster structure on $X$ is a cluster structure on the coordinate ring of $X$ such that $\{\phi, \psi\} = \text{const} \cdot \phi \psi$ whenever $\phi, \psi$ are cluster variables which belong to the same cluster. When the Poisson bivector vanishes at some point $x \in X$, the tangent space $T_x X$ comes equipped with a Poisson bracket $\{~,~\}^{\text{lin}}$, the linearization of $\{~,~\}$. Given a function $\phi$ on $X$, we propose a way of linearizing it to get a function $\phi^{\text{lin}}$ on $T_x X$. Very often, when $\{\phi_1, \cdots, \phi_n\}$ is a cluster in a log-canonical cluster structure on $(X, \{~,~\})$, $\{\phi_1^{\text{lin}}, \cdots, \phi_n^{\text{lin}}\}$ is an integrable system on $(T_x X, \{~,~\}^{\text{lin}})$. We present two scenarios where this is the case.