Mathematics

For elliptic curves, the Mordell-Weil Theorem allows to relate bisections (pre-images of the multiplication by 2) in the group of points of a curve defined over F_q and the quadratic reciprocity of some elements in the field F_q, which can be used to obtain an algorithm to bisect points in E(F_q). For reduced divisors D=[u(x),v(x)] (in Mumford representation) in the Jacobian of imaginary hyperelliptic curves y^2=f(x) (with f(x) squarefree and of odd degree), we show a relation between the existence of F_q-rational bisections and the quadratic character of u(x) when it is evaluated at the roots of the polynomial f(x) (i.e. at the x-coordinates of the Weierstrass points). This characterization allows us to compute all the bisections of a reduced divisor computing a few square roots (2g square roots if f(x) has 2g+1 roots in F_q) and solving a small system of linear equations.For hyperelliptic curves of genus 2, we obtain an equivalent characterization for curves with a real model (with f(x) squarefree of degree 6) when working with balanced divisors.

Fifty years ago Richard Kenneth Guy joined the then Department of Mathematics, Statistics and Computer Science at the nascent University of Calgary. Although he retired from the University in 1982, he has continued, even in his 100th year, to come in every day and work on the mathematics that he loves.

Hugh Williams, Richard’s long-time friend and colleague, will share with us a glimpse into the life and research of this most remarkable man. You will not want to miss this inspirational talk!

We would like to give a detailed presentation of some equations which exhibit some nonlocal phenomena. Often, the nonlocal effect is modelled by a diffusive operator which is (in some sense) elliptic and fractional. Natural example arise from probability, geometry, quantum physics, phase transition theory and crystal dislocation dynamics. We will try to discuss some of the mathematical tools that are useful to deal with these problems, explain in detail some of the main motivations, describe some recent results on these topics and list some open problems.

The Criminal Justice System is responsible for upholding public safety through the enforcement of laws, the apprehension, prosecution, and judging of suspects, and the administration of community and custodial sentences. It is highly complex, with interactions between police, prosecutors, judges, the court, and correctional services. Effective and efficient administration of justice is important for maintaining public safety.

We present an overview of operational research modelling applied to the Criminal Justice System. Two case studies are considered: a systems dynamics model of the impact of the 2010 impaired driving legislation in British Columbia and a queue network model of the impact of the Truth in Sentencing Act of Canada.

Experimental design is a branch of statistics focused upon designing experimental studies in a way that maximizes the amount of salient information produced by the experiment. It is a topic which has been well studied in the context of linear systems. However, many physical, biological, economic, financial and engineering systems of interest are inherently non-linear in nature. Experimental design for non-linear models is complicated by the fact that the optimal design depends upon the parameters that we are using the experiment to estimate. A Bayesian, often simulation-based, framework is a natural setting for such design problems. We will illustrate the use of such a framework by considering the design of an animal disease transmission experiment where the underlying goal is to identify some characteristics of the disease dynamics (e.g. a vaccine effect, or the infectious period).