**Instructor:** Monica Visan, MS 6167. Email address: visan@math.ucla.edu

**Office Hours:** Tu 1:30-2:30pm and Fri 1:30-2:30pm in MS 6167.

**Topics:**

- Concentration compactness for the Gagliardo-Nirenberg and Sobolev embedding inequalities.
- Existence of optimizers for Sobolev embedding.
- The Kakeya problem.
- Restriction theory beyond L
^{2}. - Concentration compactness for the Schrodinger propagator.
- Optimizers for the Strichartz inequality.

- J. Bourgain,
*Besicovitch type maximal operators and applications to Fourier analysis.*GAFA**1**(1991), 147-187. - R. Killip and M. Visan,
*Nonlinear Schrodinger equations at critical regularity.*To appear in Clay Mathematics Institute Summer School Proceedings. - E. Stein,
*Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals.*Princeton Mathematical Series, 43. Princeton University Press, 1993. - T. Tao,
*Restriction theorems and applications.* - T. Wolff,
*Lectures on harmonic analysis.*University Lecture Series, 29. American Mathematical Society, Providence, RI, 2003.

**Grading:** Grading will be based solely on the homework. Problems
will be assigned and collected throughout the quarter.

**Homework:** You may collaborate on the homework, but solutions need
to be written up in your own words.

- Homework 1 is due in class on Monday, Feb. 11th.
- Homework 2 is due in my mailbox by 6pm on Tuesday, March 19th.