Dr. Matthew Badger (Dept. of Mathematics, Univ. of Connecticut)

10/24/2022  4:10pm

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, which contains all the points of the set where a randomly moving particle can land. In this talk, I will present the first explicit numerical bounds on the dimension of the subset in Bourgain's theorem, obtained in joint work with Alyssa Genschaw. I will focus on the story of how we arrived at these results, the role of mathematical software, and potential for future improvements.