09/16/2026
By Joris Roos
The Department of Mathematics and Statistics invites you to attend a colloquium lecture by Matthew Badger, professor of mathematics at the University of Connecticut.
- Title: “3D Brownian motion and sets of dimension 2.999999”
- Date: Wednesday, Sept. 30
- Time: 11 a.m. – noon
- Location: Southwick Hall, Room 350W
Everyone is welcome!
Abstract
As you breathe, air eventually reaches the alveoli in your lungs. You might wonder if a particle of air is equally likely to reach all parts of your lungs. The answer is emphatically no! Mathematically, one explanation is a theorem of Bourgain, which states that for any closed set in space, there is always a subset of Hausdorff dimension less than 3 that contains all the points of the set where a randomly moving particle can land. In this talk, I will present explicit numerical bounds on the dimension of the subset in Bourgain's theorem, obtained in joint work with Michael Albert and Alyssa Genschaw. I will focus on the story of how we arrived at these results, the role of software and AI in mathematical exploration, and the potential for future improvements.