Lecture

Title: Strong Cospectrality in Trees

Title: The k-independence number of graph products

Abstract: The k-independence number of a graph is the maximum size of a set of vertices at pairwise distance greater than k, generalizing the standard independence number. In this talk, I will discuss well-known sharp bounds on the independence number of graph products, and extend some of these bounds to the k-independence number. Specifically, we will cover the Cartesian, tensor, strong, and lexicographic products.

Joint work with Aida Abiad.

Title: Box-ball systems, RSK, and Motzkin paths 

Abstract:  A box-ball system (BBS) is a discrete dynamical system whose dynamics come from the balls jumping according to certain rules. A permutation on n objects gives a BBS state by assigning its one-line notation to n consecutive boxes. After a finite number of steps, a box-ball system will reach a steady state. From any steady state, we can construct a tableau called the soliton decomposition of the box-ball system.

Title: Spectral Turan Problems on trees and even cycles

Abstract:  In this talk, we discuss some recent progress with the spectral analogue of a few Turán problems: Instead of maximizing the number of edges, our objective is to maximize the spectral radius of the adjacency matrices of graphs not containing some subgraphs.

Title: Stochastic Optimization

Abstract: While deterministic optimization problems are very useful in practice, often times the assumption that all data is known in advance does not hold true. One possible way to relax this assumption is to assume that the data depends on random variables. This assumption leads to stochastic optimization problems.

Title: Bounded treewidth in hereditary graph classes

Abstract: A highlight of the superb graph minors project of Robertson and Seymour is their so-called Grid Theorem: a minor-closed class of graphs has bounded treewidth if and only it does not contain all planar graphs. Which induced-subgraph-closed graph classes have bounded treewidth?

Title: 3-colouring via flows

Abstract: I'll show a technique to colour graphs on surfaces using max-flow min-cut.

Title: A primal-dual interior-point algorithm fo rnonsymmetric conic optimization

Abstract:

It is well known that primal-dual interior-point algorithms for linear optimization can easily be extended to the case of symmetric conic optimization, as shown by Nesterov and Todd (NT) in their 1997 paer about self-scaled barriers. Although many convex optimization problems can be expressed using symmetric cones then models involving for instance exponential functions do not belong to the class of symmetric conic optimization problems.

The profound impact of early discovery, experimentation, and disruption through research and invention

Researchers today build on the knowledge and discoveries made by those who have come before them. How can today’s researchers light the early pathways and curiosities for the research breakthroughs of the future? How can we demonstrate the impact and potential of the yet-to-be known? And, what if any, role does academia, industry, the Faculty of Mathematics, and Canada play in increasing the discovery journey to these new frontiers?

The "blood, sweat, tears, toil and triumphs" of commercializing technology

Marc Morin is the co-founder and CEO of Auvik Networks, creators of cloud-based software that makes it dramatically easier for IT managed service providers to monitor and manage their clients' IT networks. A serial entrepreneur, Marc has previously co-founded several successful companies, including PixStream (acquired by Cisco for USD$369 million) and Sandvine (Sold to Francisco Partners for CAD$582 million), and is a seed investor in a number of local tech companies.