University of Lethbridge

It is known that if the negative Pell equation X2−DY2=−1 is solvable (in integers), and if (x,y) is its solution with smallest positive x and y, then all of its solutions (xn,yn) are given by the formula xn + yn√D = ±(x + y√D) 2n+1 for n∈Z...

A Hadamard matrix H of order 4n2 is said to be skew-regular if it is of skew-type and the absolute values of the row sums are all 2n. It is conjectured that for each odd integer n there is a skew-regular matrix of order 4n2. A Hadamard matrix H of...

In this talk I will consider the discrete moments J_k(T) that are defined by summing the 2k-th power of the absolute value of the derivative of the Riemann zeta function zeta(s) at all nontrivial zeros of zeta(s) whose imaginary part has absolute...

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...

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...

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...

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...

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...

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...

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)...