Reading Materials
Papers
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations [PDF]
- Global Well-Posedness for a periodic nonlinear Schrödinger equation in 1D and 2D [PDF]
- The distribution of lattice points in elliptic annuli [PDF]
- Bourgain: On Strichartz's Inequalities and the Nonlinear Schrodinger Equation on Irrational Tori [PDF]
- Nowak: Primitive Lattice Points Inside an Ellipse [PDF]
- Bourgain: Approximation of Solutions of the Cubic Nonlinear Schrodinger Equations by Finite-Dimensional Equations and Nonsqueezing Properties [PDF]
- Kuksin: Infinite-Dimensional Symplectic Capacities and a Squeezing Theorem for Hamiltonian PDE's [PDF]
- Bounds on the Growth of High Sobolev Norms of Solutions to the 2D Defocusing Periodic Cubic NLS [PDF]
- Global Well-Posedness for a Periodic Nonlinear Schrodinger Equation in 1D and 2D [PDF]
- Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation [PDF]
- Periodic Nonlinear Schrodinger Equation and Invariant Measures [PDF]
- Invariant Weighted Wiener Measures and Almost Sure Global Well-Posedness for the Periodic Derivative NLS [PDF]
- Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations [PDF]
Class Lecture Notes
- Lecture 1 [PDF]
- Lecture 2 [PDF]
- Lecture 3 [PDF]
- Lecture 4 [PDF]
- Lecture 6 [PDF]
- Lecture 7 [PDF]
- Lecture 8 [PDF]
- Lecture 9 [PDF]
- Lecture 10 [PDF]
- Lecture 11 [PDF]
- Lecture 12 [PDF]
- Lecture 13 [PDF]
- Lecture 14 [PDF]
- Lecture 15 [PDF]
- Lecture 16 [PDF]
- Lecture 17 [PDF]
- Lecture 18 [PDF]
- Lecture 19 [PDF]