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

**Office Hours:** Mon 3:00pm-4:00pm.

**Topics:**

- Restriction theory.
- Rearrangement inequalities.
- Optimizers and sharp constants for the Gagliardo-Nirenberg and Sobolev embedding inequalities.

- A. Burchard,
*Rearrangement inequalitites.*Lecture notes available online. - R. Killip and M. Visan, Nonlinear Schrodinger equations at critical regularity. In "Evolution Equations", 325-437, Clay Math. Proc., 17, Amer. Math. Soc., Providence, RI, 2013.
- E. Lieb and M. Loss,
*Analysis*. AMS Graduate Studies in Mathematics, 14 (1987, second edition 2001). - E. Stein,
*Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals.*Princeton Mathematical Series, 43. Princeton University Press, 1993.

**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.