University of Lethbridge

Graphical and Digraphical Regular Representations (GRRs and DRRs) are a concrete way to visualise the regular action of a group, using graphs. More precisely, a GRR or DRR on the group G is a (di)graph whose automorphism group is isomorphic to the...

Given an abelian variety A defined over a number field, a conjecture attributed to Serre states that the set of primes at which A admits ordinary reduction is of positive density. This conjecture had been proved for elliptic curves (Serre, 1977)...

In 1992, Erd˝os, Granville, Pomerance, and Spiro conjectured that if A is a set of integers with asymptotic density zero then the preimage of A under s(n), sum-of-proper-divisors function, also has asymptotic density zero. In this talk, we will...

Harary and Sabidussi were the first to study the automorphisms of repeated graphs using the wreath product. Later Hemminger would go on to provide necessary and sufficient conditions for these of repeated automorphisms through the introduction of...

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...

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...

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...

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...

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...