1. On Rearrangements of Fourier Series Mark Lewko TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A AAA A AAA A A A A A A On the distribution of values of orthonormal systems with restricted supports

2. Orthonormal System

3. Meta-Question Given: What can we say about:

4. Random versus Explicit Sharp (or nearly sharp) results Stochastic processes Metrical entropy A lot of work to marginally beat trivial estimates Analytic number theory (circle method) Fourier restriction theory (multi- linear estimates) Combinatorics (sum-product estimates) ? ABC Conjecture / PFR conjecture / Faltings theorem ?

5. (Random) No explicit examples (unless p is even integer)

6. Finite Field Restriction Estimates

7. Compressed Sensing

8. Compressed Sensing II

9. Rearrangements of Fourier Series Kolmogorov (1920’s)

10. Rearrangements of Fourier Series II Rademacher-Menshov Bourgain

11. Rearrangements of Fourier Series III

12. Thank You!