Keynote speakers

Title: Representing everything (or:  how representation theory rules the world)

Language: English

Abstract: Mathematics is often about understanding objects through their symmetries.  But what do you do when the group of symmetries is nightmarishly complicated?  Answer: You turn the problem into one where you can apply math’s ultimate weapon: linear algebra.  This process is called representation theory, and it has applications everywhere from number theory, to physics, to the development of space-time codes.  We’ll use these examples to share some of the successes, and some of the open problems, of representation theory today; by the end, you, too, will be representing everything. 

Presentation date: Thursday, May 23rd

Professor Monica Nevins obtained her PhD from MIT in 1998.  After two years as a Killam Postdoctoral Fellow at the University of Alberta, she joined the University of Ottawa, where she has supervised over 25 graduate students and 30 undergraduate research projects.  Her research interests are in the representation theory of p-adic groups, and in the applications of representation theory and algebra to cryptography and codes.  She was awarded the University of Ottawa Award for Excellence in Teaching in 2011 and was named a Fellow of the Canadian Mathematical Society in 2019. 

Title: Progress on Pursuit-Evasion Games on Graphs

Language: English

Abstract: In pursuit-evasion games on graphs, a set of pursuers attempts to locate or eliminate the threat posed by an evader in the network. The rules greatly determine the difficulty of the game; for example, the evader may be visible, but the pursuers may have limited movement speed, only moving to nearby vertices adjacent to them. A central theme is the optimization of certain parameters, such as the cop number, burning number, or localization number. Finding the exact values, bounds, and algorithms to compute these graph parameters leads to fascinating topics intersecting with classical graph theory, combinatorial designs, and probabilistic methods. We'll survey some of these topics in the talk.

Presentation date: Wednesday, May 22nd

Dr. Anthony Bonato's research is in graph theory and network science. He authored over 150 papers with over 120 co-authors. He is the author of five books, with the most recent one, An Invitation to Pursuit-Evasion Games and Graph Theory, published by the American Mathematical Society in 2022. Dr. Bonato is currently a full Professor in the Department of Mathematics at Toronto Metropolitan University. 

Title: Some applications of machine learning methods in survey sampling 

Language: English

Abstract: In the last decade, the interest in machine learning methods has been growing in national statistical offices (e.g., Statistics Canada). These data-driven methods provide flexible tools for obtaining accurate predictions. The increasing availability of data sources (e.g., big data sources and satellite information) provides a rich pool of potential predictors that may be used to obtain a set of predictions at different stages of a survey. These stages include the nonresponse treatment stage (e.g., propensity score weighting and imputation) and the estimation stage (e.g., model-assisted estimation and small area estimation). In this talk, I will give an overview of the potential use of machine learning procedures in national statistical offices. 

Presentation date: Friday, May 24th

David Haziza is Professor in the Department of Mathematics and Statistics. His research interests include the treatment of missing data, the problem of inference in the presence of outliers, resampling method and machine learning methods. Since 2006, he’s a consultant at Statistics Canada. 

Title: New Approaches to Complexity via Quantum Graphs  

Language: English

Abstract: Problems based on the structure of graphs -- for example finding cliques, independent sets, or colourings -- are of fundamental importance in classical complexity. It is well motivated to consider similar problems about quantum graphs, which are an operator system generalisation of graphs. Defining well-formulated decision problems for quantum graphs faces several technical challenges, and consequently the connections between quantum graphs and complexity have been underexplored. 

In this work, we introduce and study the clique problem for quantum graphs presented as quantum channels. We show that the quantum clique problem is QMA(2)-complete. This problem is the natural quantisation of an NP-complete problem, which provides a classical complexity problem whose natural quantisation is QMA(2), rather than QMA, which is commonly assumed.

This presentation is based on joint work with Arthur Mehta.

Presentation date: Wednesday, May 22nd

The Outstanding Student Paper Prize recognizes outstanding scholarly work of students in the Department of Mathematics and Statistics at the University of Ottawa. Eric Culf is one of the 2022 recipients of this prize, awarded for work done during his M.Sc. at the University of Ottawa under the supervision of Professor Anne Broadbent.