University of Lethbridge

The Traveling Salesman Problem asks for the shortest route through a collection of cities. This classical problem is very hard, but, by applying Linear Programming (and other techniques), the optimal route has been found in test cases that have tens...

Twin prime powers are used in the construction of some very interesting combinatorial objects. In an old paper they are used in the construction of regular Hadamard matrices. In a recent work, they are used to show the existence of an infinite class...

In 1909, Landau showed that the lim sup of the quotient of n by ϕ(n) log log n is exp(γ), where ϕ(n) is Euler's function. Later, Rosser and Schoenfeld asked whether there were infinitely many n for which n/ϕ(n) is greater than (log log n) exp(γ)...

An "elliptic sequence" is a solution over an arbitrary integral domain of the recursion W(m+n) W(m-n) = W(m+1) W(m-1) W(n)^2 - W(n+1) W(n-1) W(m)^2, where m and n are integers. The theory of integral elliptic sequences was developed by Morgan Ward in...

How many lines may one arrange through the origin in R10 in such a way that any two of them are at least 89° apart? How about in R57? Or Rn as n tends to infinity? Using this simply stated problem as a point of departure, I will explore various areas...

In this talk, we review some classic iterative processes: Mann iterative process, Ishikawa iterative process, Halpern iterative process, Viscosity iterative process, hybrid projection iterative process, for solutions of operator equations involving...

Let K/k be a Galois extension of number fields with Galois group G, and let rho be a non-trivial irreducible representation of G of dimension n. The Artin holomorphy conjecture asserts that the Artin L-function attached to rho extends to an entire...

In the late 1930s, Paul Erdos attended a seminar at Cornell University given by Mark Kac, who suspected that divisibility by primes satisfies a certain "statistical independence" condition. If this were true, the central limit theorem could be used...

I will discuss the connections between metric Diophantine approximation and the construction of measures whose Fourier transform decays as fast as possible (relative to the Hausdorff dimension of the support of the measure). Concepts like Diophantine...

Primality testing has a number of important applications. In particular in cryptographic applications the complexity of existing deterministic algorithms causes increasing latency as the size of numbers we must test grow and the number of tests we...