Colloquium Talk Dr. Paul Voutier: Explicit Effective Diophantine Approximation

The Department of Mathematics and Statistics would like to invite graduate students as well as anyone else interested to a talk by Dr. Paul Voutier entitled Explicit Effective Diophantine Approximation. The talk will take place on Friday January 10 from 3:00 PM to 4:00 PM and be held in Goodman School of Business room 408. This lecture will be accessible to graduate students,and even enthusiastic advanced undergraduates.

Diophantine problems go back to the early days of civilisation. Our earliest written evidence of such problems is found on the famous Babylonian clay tablet, Plimpton 322, dating back to 1800BC. Diophantine problems continue to play an important role up to the present day with the use of elliptic curves in cryptography. There are several categories of diophantine results. We speak of qualitative, quantitative, elective and explicit elective results. In this lecture, we focus on the last of these: explicit elective results. Under certain conditions, we can obtain very good explicit bounds on how well we can approximate some interesting irrational numbers by rational numbers. That is the goal of this lecture: providing a clear presentation of such techniques, while also providing insights into the latest and sharpest results in this area.