Current students

Title: Vertex-minors and sparsity

Abstract:

We discuss an ongoing project with Jim Geelen and Paul Wollan to describe the structure of graph classes excluding a vertex-minor.

Title: Combinatorial Hall algebras

Abstract:

The Hall algebra of a finitary category is an associative (and sometimes Hopf) algebra whose structure constants count the number of extensions between objects.

Title: Linear Programming and Extremal Expanders

Abstract:

Nozaki proved a linear programming bound on the number of vertices that depends on the eigenvalues of a graph.

Title: Excluding an asymmetric group labelled graph

Abstract:

There are several models of group labelled graphs. In the simpler, undirected model, for an abelian group Γ, every edge e receives a label γ(e) in Γ. 

Title: An equivariant basis for the cohomology of Springer fibers

Abstract:

Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this talk, I will discuss joint work with Martha Precup where we analyze the equivariant cohomology of Springer fibers in type A.

Title: Triangle-free Strongly Regular Graphs

Abstract:

Complete bipartite graphs aside, only five triangle-free strongly regular graphs are known. I will describe some of the background to this topic, with the focus on outlining the construction of the Higman-Sims graph.

Title: Parallel strategies for SIDH: towards computing SIDH twice as fast

Abstrtact:

Over the last ten years, there has been an intense research effort to find hard mathematical problems that would be presumably hard to solve by a quantum attacker and at the same time could be used to build reasonably efficient public-key cryptoschemes.

Title: A generalization of balanced tableaux and matching problems with unique solutions

Abstract:

In this talk, we consider families of finite sets that we call shellable and that have been characterized by Chang and Hirst and Hughes as being the families of sets that admit unique solutions to Hall's matching problem.

Title: Moore Graphs

Abstract:

Moore graphs were introduced by Hoffman and Singleton in a fundamental paper. They can be defined as graphs with diameter $d$ and girth $2d+1$.

Title: List Colouring and Ohba's Conjecture

Abstract:

The question of when the list-chromatic number of a graph G, denoted chi_l(G), equals its chromatic number is fundamental to the theory of list colouring.