Connor Stevens

Fourier Transforms of nonlinear Markov map invariant measures

The Fourier transform of a function immediately motivates the definition of the Fourier transform of a measure. I will introduce this object, and explain why we are particularly interested in when we get polynomial decay for the transform. The history in this area suggests that nonlinear map invariance of a measure should be sufficient to give polynomial decay. I plan to justify this by presenting the two main tools in Ergodic theory and additive combinatorics that allude to such decay. Joint work with Tuomas Sahlsten.