Reading seminar on Fractal Uncertainty Principle
Autumn 2018, University of Manchester
Motivated by the Heisenberg Uncertainty Principle in quantum physics and signal processing, the Fractal Uncertainty Principle states that no signal cannot be localised in both time and frequency into a fractal set. This semiclassical method has numerous recent applications in open dynamical systems, quantum chaos and scattering theory. Moreover, the proof of FUP for various fractals relies on modern tools from additive combinatorics and Fourier analysis. The reading seminar aims to go through this topic and discuss related notions.
Time and date: Roughly bi-weekly at 1 pm on Mondays in Frank Adams 2, Alan Turing Building.
- 1st October, 2018: Tuomas Sahlsten: Definition of FUP, connections to additive combinatorics, Fourier decay and open dynamical systems, notes
- 15th October, 2018: Borys Kuca: Introduction to additive energy
- 5th November, 2018: Sean Holman: Introduction to semiclassical analysis
- 12th November, 2018: Connor Stevens: Additive energy and Fourier decay
Semyon Dyatlov: Notes on Fractal Uncertainty Principle (version 0.5, pdf)
+ references within the notes
Analysis Aspects of Dynamics conference
Spring 2018, Imperial College London
Analysis Aspects of Dynamics
Imperial College London, May 16-18, 2018
Supported by London Mathematical Society, EPSRC and the Imperial College London