Quantifications of the Besicovitch Projection theorem in a nonlinear setting
Ergodic Theory and Dynamical Systems Seminar
11th March 2021, 4:30 pm – 5:30 pm
Online via Zoom, (if interested, please email one of the organisers to gain access to the Zoom link)
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 discuss 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.