Past Events

A G2-structure is a special type of 3-form on an oriented 7-manifold, which determines a Riemannian metric in a nonlinear way. The best class of such 3-forms are those which are parallel with respect to their induced Levi-Civita connections, which is...

Recent advances in single cell sequencing has led to the availability of gene expression data. We model the trajectories of cells in gene expression space using a diffusion and gradient drift process that also undergoes branching. In this talk, we...

Although my talk is arguably about machine-learning, I will use mostly ideas and language from mathematical modelling and numerical analysis. I will introduce a natural geometric learning framework, the atomic cluster expansion (ACE), which focuses...

The adjacency matrix A of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. If u and v are distinct vertices in G, we say perfect state transfer from u to v occurs if there is a time t such that the (u,v)-entry of...

A set $\{a_{1}, a_{2},\ldots, a_{m}\}$ of distinct positive integers is a Diophantine $m$-tuple if the product of any two distinct elements in the set is one less than a square. There is a long history and extensive literature on the study of...

Quadratic form theory started as a part of number theory; people were notably interested in representation questions, such as which number of a given field can be written as a sum of a certain number of squares. In the 1930’s, Witt started the...

Projection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. We will...

Let $\sigma^*(n)$ be the sum of all unitary (i.e. coprime) divisors of $n$. As an analogue of Lehmer’s totient problem, Subbarao proposed the following conjecture. The congruence $\sigma^*(n)\equiv 1\pmod{n}$ is possible iff $n$ is a prime power...

Given a graph H, say that a graph G is properly rainbow H-saturated if there exists a rainbow H-free proper edge-colouring of G and, for any non-edge e of G, every proper edge-colouring of G+e contains a rainbow copy of H. The proper rainbow...

The action of the automorphisms of a formal group on its deformation space is crucial to understanding periodic families in the homotopy groups of spheres and the unsolved Hecke orbit conjecture for unitary Shimura varieties. We can explicitly pin...