Math/Stats Colloquium: Michelle Mastrianni '16
Tue, April 18, 2023 • 3:30pm - 4:30pm (1h) • CMC 206
Title: Discrepancy theory: approximating continuous objects by discrete distributions
Abstract: If I asked you to place N points evenly on a unit interval, you would likely be able to do so with no hesitation. Increase the dimension of the space, however, and the question of how to find a "most uniform" N-point set in such a space (e.g. the d-dimensional unit cube, or the surface of a sphere) becomes much more difficult. This talk will introduce the notion of the "discrepancy" of a finite point set, which is a measure of its irregularities of distribution. We will discuss examples of some elegant analytic techniques used in the study of discrepancy. More generally, we'll survey some intriguing results and open problems in the field, which have connections to a variety of areas of mathematics such as approximation theory, discrete geometry, number theory, and probability.