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

**Office Hours:** just walk in.

**Topics:** We investigate local and global properties of solutions
to the focusing Klein-Gordon equation in three space dimensions, with
emphasis on the blowup/scattering dychotomy. The lectures will cover

- Strichartz estimates and local well-posedness.
- The groundstate solution.
- The Payne-Satinger criterion.
- Scattering "below" the groundstate.
- Center, stable and unstable manifolds in hyperbolic dynamics.
- The Lyapunov-Perron and Hadamard methods.
- The one-pass theorem.

- K. Nakanishi and W. Schlag,
*Invariant manifolds and dispersive Hamiltonian evolution equations.*Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zurich, 2011.

**Homework:** There will be a small number of homework problems, whose completion is required to pass the class.

**Homework problems:**