Tuesday, April 25, 2023 - 3:45pm to 4:45pm
University of British Columbia
The ancient Pythagorean theorem gives a formula for computing the Euclidean distance between two points. It is simply astounding that a concept so simple and classical has continued to fascinate mathematicians over the ages, and remains a tantalizing source of open problems to this day. Given a set E, its distance set consists of numbers representing distances between points of E. If E is large, how large is its distance set? How does the structure of a set influence the structure of distances in the set? Such questions play an important role in many areas of mathematics and beyond. The talk will survey a few research problems associated with Euclidean distances between points and discuss recent breakthroughs in some of them. The presentation is intended to be an introduction to a vibrant research area; no advanced mathematical background will be assumed.