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Mathematics

Bisections and Squares in Hyperelliptic Curves

Speaker: 
Nicolas Theriault
Date: 
Fri, Jun 10, 2016
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 
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.

The Life and Numbers of Richard Guy

Speaker: 
Hugh Williams
Date: 
Tue, Jun 21, 2016
Location: 
PIMS, University of Calgary
Conference: 
Canadian Number Theory Association 2016
Abstract: 
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!

Nonlocal equations from various perspectives - lecture 3

Speaker: 
Enrico Valdinoci
Date: 
Wed, Jun 15, 2016
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Workshop on Nonlocal Variational Problems and PDEs
Abstract: 
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.

Nonlocal equations from various perspectives - lecture 2

Speaker: 
Enrico Valdinoci
Date: 
Tue, Jun 14, 2016
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Workshop on Nonlocal Variational Problems and PDEs
Abstract: 
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.

Nonlocal equations from various perspectives - lecture 1

Speaker: 
Enrico Valdinoci
Date: 
Mon, Jun 13, 2016
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Workshop on Nonlocal Variational Problems and PDEs
Abstract: 
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.

Operational Research and the Criminal Justice System

Speaker: 
Alexander Rutherford
Date: 
Wed, Mar 30, 2016
Location: 
PIMS, Simon Fraser University
Conference: 
Lunchbox Lecture Series
Abstract: 
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.

A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications.

Speaker: 
Mark Goresky
Date: 
Mon, May 30, 2016
Location: 
PIMS, University of British Columbia
Conference: 
2016 Niven Lecture
Abstract: 
During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes. The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications. The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described.
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