Math 8110

Textbook:
There is no official textbook for the course, but I will use the
following notes

- T.
Wolff: Fourier Analysis

- Bouchlet: Short introduction to dispersive PDE
- E. M. Stein: Harmonic Analysis

- R. C. Vaughan: The circle method

Description:
The aim of the course is to give an introduction to Fourier
Analysis and to some of its applications to PDE and Number Theory.
Possible topics included but are subject to change.

- The Fourier transform on L^1 and L^2. Plancherel's theorem.

- The Schwarz space and tempered distributions.

- Complex and real interpolation methods. The Hausdorff-Young
theorem.

- The uncertainty principle. The method of stationary phase.
- Fourier restriction and maximal operators along surfaces.
- Linear and non-linear Schrodinger equation.
- Fourier analysis on the integer lattice. The circle method.

- Fourier transforms of integer points on varieties.
- Fourier restriction and maximal operators in the discrete setting.

The lectures are uploaded here:

Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5-6 Lecture 7-8 Lecture 9 Lecture 10-11 Lecture 12

Lecture 13 Lecture 14-15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21