University of Lethbridge

This is a continuation of last week's talk. I will sketch Matti Jutila's proof of a subconvex bound for a modular L-function on the critical line. The main ideas are an approximate functional equation, the use of Farey fractions, Voronoi's summation...

In this talk we will show how to exhibit large and small gaps between the zeros of the Riemann zeta function, assuming the Riemann hypothesis. This is based on a technique of Montgomery and Odlyzko. The problem of finding small gaps between the zeros...

The purpose of the Alberta Mathematics Dialogue is two-fold. In the one hand it promotes mathematical research across universities in the Province of Alberta and on the other hand it serves as a forum for discussing issues related to mathematical...

Let A denote the algebra of all linear operators on a complex vector space V—mostly finite-dimensional for the purposes of this talk. Let G be an irreducible group or semigroup contained in A. (This means that there is no subspace of V other than {0}...

The classical problem of Diophantine equations is to solve polynomial equations over the rationals. More generally, we may consider solutions over an extension of the rationals. If the equations define an elliptic curve (or more generally, an Abelian...

Let A denote the algebra of all linear operators on a complex vector space V—mostly finite-dimensional for the purposes of this talk. Let G be an irreducible group or semigroup contained in A. (This means that there is no subspace of V other than {0}...

The classical problem of Diophantine equations is to solve polynomial equations over the rationals. More generally, we may consider solutions over an extension of the rationals. If the equations define an elliptic curve (or more generally, an Abelian...

In this talk, we will highlight the importance of measurement, and discuss what can and cannot be measured. Focusing on the measurement of position, importance, and shape, we will illustrate by discussing the mathematics behind GPS, Google and laser...

A number $n$ is called squarefull if for every prime $p$ dividing $n$, we have $p^2$ also dividing $n$. Erdos conjectured that the number of pairs of consecutive squarefull numbers $(n, n+1)$ with $n N$ is at most $(log N)^A$ for some $A >0$. This...

Let $a \in \mathbb{Z} \setminus \{0,\pm 1\}$, and let $f_{a}(p)$ denote the order of $a$ modulo $p$, where $p \nmid a$ is prime. There are many results that suggest $p - 1$ and $f_{a}(p)$ are close. For example, Artin's conjecture and Hooley's...