Mathematics Colloquium via Zoom

Nonlinear projection theory in geometry and harmonic analysis

Dr. Krystal Taylor

The Ohio State University

Abstract: There are many classical results relating the geometry, dimension, and measure of a set to the structure of its orthogonal projections. It turns out that many nonlinear projection-type operators also have special geometry that allows us to build similar relationships between a set and its “projections,” just as in the linear setting. We will dis- cuss a series of recent results from both geometric and probabilistic vantage points. In particular, we will see that the multi-scale analysis techniques of Tao, as well as the energy techniques of Mattila, can be strengthened and generalized to projection-type operators satisfying a transversality condition. As an application, we find upper and lower bounds for the rate of decay of the Favard curve length of the four- corner Cantor set.

Zoom ID: 936 2657 5714

Passcode available upon request

Free