University of Lethbridge

Associating graphs with groups date back to Arthur Cayley. In this lecture, we will discuss about another graph, called co-maximal subgroup graph Γ( G) introduced by Akbari et al. in [1]. The co-maximal subgroup graph Γ( G) of a group G whose...

In this talk I will present a study on the Gromov's hyperbolicity of some product of graphs. The presentation is based on joint works that studied hyperbolicity of the lexicographic product, tensor product and graph join of two graphs, respectively...

A perfect matching (   P M ) in the complete graph K 2 k K 2 k is a set of edges by which every vertex is covered exactly once. Two   P M s are said to be t t -intersecting if they have at least t t edges in common. Another type pf intersection...

Consider a group G acting transitively on the vertices of an infinite, cubic (3-regular) graph Gamma such that the vertex stabilizers are infinite. We will see that if G is also edge-transitive on Gamma, then Gamma is the infinite cubic tree, and if...

A power series f(x1,…,xm)∈C[[x1,…,xm]] is said to be D-finite if all the partial derivatives of f span a finite dimensional vector space over the field C(x1,…,xm). For the univariate series f(x)=∑anxn, this is equivalent to the condition that the...

The blow up of the anticanonical base point on X, a del Pezzo surface of degree 1, gives rise to a rational elliptic surface E with only irreducible fibers. The sections of minimal height of E are in correspondence with the 240 exceptional curves on...

It is an open question of Baker whether the Dirichlet L-values at 1 with fixed modulus are linearly independent over the rational numbers. The best-known result is due to Baker, Birch and Wirsing, which affirms this when the modulus of the associated...

It is a classical problem to understand the set of Jacobians of curves among all abelian varieties, i.e., the image of the map Mg→Ag which sends a curve X to its Jacobian JX. In characteristic p, Ag has interesting filtrations, and we can ask how the...

In 1944, Linnik showed that the least prime in an arithmetic progression given by a mod q for (a,q)=1 is at most cq^L for some absolutely computable constants c and L. A lot of work has gone in computing explicit bounds for c and L. The best known...

We will discuss a graph that encodes the divisibility properties of integers by primes. We prove that this graph has a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the traditional...