University of Lethbridge

L-functions associated with automorphic forms are vast generalizations of Riemann zeta functions and Dirichlet L-functions. Although the theory of L-functions play a fundamental role in number theory, it is still largely conjectural. If π is an...

What happens when you add up the divisors of an integer? This seemingly innocuous question has motivated mathematicians across the ages, from antiquity to the present day. In this talk, we'll survey some conjectures and results on the functions s(n)...

Siegel zeros (or Landau-Siegel zeros) are potential counterexamples to the generalised Riemann hypothesis (for L-functions). Such zeros, if exist, have to be "very close" to 1 over the complex plane. In this talk, we will discuss some results...

A Digraphical Regular Representation (DRR) for a group G is a directed graph whose full automorphism group is the regular representation of G. In 1981, Babai showed that with five small exceptions, there is at least one DRR for every finite group. A...

We describe various models of creating communities of mathemati- cal explorers, inspired by our work at Illinois and Washington, and earlier work at Maryland. We will outline how we think any Math department can be the center of a vibrant...

In joint work with David Aulicino and Pat Hooper, we study the problem of finding closed geodesics passing through exactly one vertex on the surfaces of Platonic solids. We show that there are no such trajectories on any of the solids except the...

The Math Catcher Outreach program aims to promote mathematics and scholarship in general by encouraging elementary and high school students to recognize how math is used in everyday life and how it forms the basis for many of our daily decisions and...

We will discuss the Cohen-Lenstra heuristics, both in the classical and non-abelian setting. In particular we will make the connection between these heuristics and the problem of counting extensions of quadratic fields with fixed Galois groups, and...

Dirichlet's theorem on arithmetic progressions states that for any (a,q)=1, there are infinitely many primes congruent to a modulo q. Such a theorem together with Euler's earlier work on the infinitude of primes represents the beginning of the study...

For every generating set S of any finite group G, there is a corresponding Cayley graph Cay(G;S). It was conjectured in the early 1970's that Cay(G;S) always has a hamiltonian cycle, but there has been very little progress on this problem. Joint work...