Title: Geometry of Sets and Harmonic Analysis
Speaker: Krystal Taylor (OSU)
Abstract:
Harmonic analysis can be used to study a number of interesting geometric problems, to name a few: obtaining error estimates for lattice point counting problems, obtaining dimensional inequalities on the intersections of fractal sets, determining which geometric configurations exists within sufficiently ``large'' subsets of Euclidean space. We look at a series of related results and questions with the aim of introducing applications of Harmonic analysis to geometric problems. We will use a lower bound on the Hausdorff dimension of a subset of Euclidean space to make precise the notion of sufficient structure or size.
Background and examples are provided, as well as open problems.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn and Spring semesters. Pre-candidacy students can sign up for this lecture series by registering for one or two credit hours of Math 6193, Call/Class # 17170 (with Prof H. Moscovici).