Speaker
Semyon Dyatlov, MIT
Abstract
Fractal uncertainty principle (FUP) is an estimate on the \(L^2\) operator norm of \(1_X B_h 1_Y\) where \(X,Y\) are fractal sets down to some small scale \(h\) and
\(B_h\) is a unitary operator whose integral kernel oscillates at wave length \(h\). This has applications to quantum chaos, including spectral gaps for convex co-compact hyperbolic surfaces. Many FUP results are available, typically reducing the case of general \(B_h\) to the Fourier transform. In this talk I will give a new FUP with a reasonably large exponent for \(1/2\)-dimensional sets \(X,Y\), relying on the difference between the operator \(B_h\) used for hyperbolic surfaces and the Fourier transform. The key ingredients come from projection theory. Joint work with Alex Cohen, and some help from AI.