University of Lethbridge

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...

A transversal of a latin square of order n is a subset of entries picked in such a way that each row, each column and each symbol is present at most once. In many latin squares, you can find a full transversal by selecting n entries which do not...

Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester.

This talk will be in two parts. It will begin with a short discussion of recent developments in the Sage Mathematics Software and some of the implications these developments may have for research in number theory world-wide. The second portion of...

In combinatorial geometry (and engineering), it is important to know that certain scaffold-like geometric structures are rigid. (They will not collapse, and, in fact, have enough bracing that they cannot be deformed at all.) Replacing the geometric...

It a classical open problem in Operator Theory whether every bounded linear operator T on a Hilbert space H has a non-trivial invariant subspace (that is, a subspace Y of H such that TY is contained in Y; nontrivial means not {0} and not H). This is...

In this talk, we discuss some results on the non-vanishing in p-adic families of the central values of certain Rankin-Selberg L-functions (namely, anticyclotomic twists of L-functions) associated to automorphic forms on GL(2).