Finite point configurations in thin subsets of Euclidean space
When
12:30 p.m., Feb. 8, 2022
The question we ask is, how large does a Hausdorff dimension of a compact subset of Euclidean space need to be to ensure that it contains vertices of a given geometric configuration like an equilateral simplex, a chain, or a loop? This problem and its variants involve an interplay of ideas from analysis, combinatorics, and number theory. We are going to describe some recent results with an emphasis on the universality of some of the underlying ideas across the various analytic, discrete, and arithmetic settings.
Place: Hybrid, Math, 402 and Zoom: https://arizona.zoom.us/j/81150211038 Password: “arizona” (all lower case)