Seminar • Algorithms and Complexity • Fun with Diophantine Approximation

Please note: This seminar will take place in DC 2310 and online.

Ingrid Vukusic, Postdoctoral Researcher
David R. Cheriton School of Computer Science

Let’s play around with some numbers and make them cancel each other out. For example, 2*2*9/(6*6) = 1. We call the triple of numbers (2,9,6) multiplicatively dependent. Now here is a little Diophantine problem: Can you find integers 1<a<b<c such that (a,b,c) and (a+1,b+1,c+1) are both multiplicatively dependent?

This problem per se is not a question of Diophantine approximation (“How well can real numbers be approximated by rational ones?”). However, in my talk, I will explain how methods and results from the field of Diophantine approximation are used to solve problems such as the above. I will give an introduction to Diophantine approximation, and, in particular talk about lower bounds for linear forms in logarithms and continued fractions. I will also make connections to metric number theory, which asks about properties of “almost all real numbers”.

To attend this seminar in person, please go to DC 2310. You can also attend virtually using Zoom.