Simon Fraser University

Recent and rapid breakthroughs in contemporary biology, climate science, and data science have unveiled a spectrum of intricate mathematical challenges which can be tackled through the fusion of applied and numerical analysis, as well as optimisation...

How many ways are there to write a given permutation as a product of m transpositions (i_1, j_1) (i_2, j_2) \dots (i_m, j_m)? For example, there are three ways to write (1,2,3) as a product of two transpositions: (1,2)(1,3), (1,3)(2,3) and (2,3)(1,2)...

I will be presenting a frame approach for computing solutions of differential equations inspired by recent progress in frame theory and sparse spectral methods. The primary case study for our method will be a very general family of equations...

The Direct Summand Theorem states that if $R$ is a commutative Noetherian ring, then any finite extension $R\to S$ splits as a map of $R$-modules. This suggests the notion of a splinter as a class of singularities, where we say a scheme $X$ is a...

Conway-Coxeter friezes are arrays of positive integers satisfying a determinantal condition, the so-called diamond rule. Recently, these combinatorial objects have been of considerable interest in representation theory, since they encode cluster...

The Deligne-Mumford compactification, $\overline{M_{0,n}}$, of the moduli space of $n$ distinct ordered points on $\mathbb{P}^1$, has many well understood geometric and topological properties. For example, it is a smooth projective variety over its...

For integers k>=1 and n>=2k+1, the Kneser graph K(n,k) has as vertices all k-element subsets of an n-element ground set, and an edge between any two disjoint sets. It has been conjectured since the 1970s that all Kneser graphs admit a Hamilton cycle...

In the past decade, (artificial) neural networks and machine learning tools have surfaced as game changing technologies across numerous fields, resolving an array of challenging problems. Even for the numerical solution of partial differential...

This is joint work with Uriya First. If $R$ is a ring and $n$ is a natural number, then an Azumaya algebra of degree $n$ on $R$ is an $R$-algebra such that $A$ becomes isomorphic to the $n \times n$ matrix algebra after some faithfully flat extension...