## Harmonic Analysis

Math 8110

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

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.
• The 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.
• Bourgain's polynomial ergodic theorem
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