Kiril Datchev

I am a fifth year PhD student in the UC Berkeley math department. My thesis advisor is Maciej Zworski. I study microlocal analysis, scattering theory, and dispersive PDE. This page has contact information.

I plan to graduate in May 2010, and am on the market for academic jobs. Here are my CV and research statement.

In Fall 2009, the Student Harmonic Analysis and PDE Seminar meets Tuesdays from 3:40 to 5:30 in 740 Evans.

1. Resonance free regions for nontrapping manifolds with cusps.

   I study the meromorphic continuation of the cutoff resolvent for a class of nontrapping manifolds with a cusp and a funnel. I prove the existence of a logarithmically large region in which the continuation is holomorphic. Slides from a talk on the subject.

2. Solitary waves for the Hartree equation with a slowly varying potential (with Ivan Ventura).

   For certain nonlinear Schrödinger equations we prove that solitons are stable under perturbation by a slowly varying potential. We show further that under the influence of this potential the soliton center of mass obeys a classical equation of motion. Slides from a talk on the subject.

3. Fast soliton scattering by attractive delta impurities (with Justin Holmer), published in Communications in Partial Differential Equations, Vol. 34, No. 9, pp. 1074-1113 (2009).

   We study the one-dimensional cubic nonlinear Schrödinger equation, and show that a delta function potential splits a rapidly moving soliton into two parts. These two parts, a transmitted and a reflected soliton, are described explicitly. Slides from a talk on the subject.

4. Local smoothing for scattering manifolds with hyperbolic trapped sets, published in Communications in Mathematical Physics, Vol. 286, No. 3, pp. 837-850 (2009).

   I study the Laplace operator on a noncompact manifold which has asymptotically Euclidean structure near infinity. I prove dispersive estimates under the assumption that only a 'small' family of geodesics remains trapped for all time in a compact set.

A perturbative approximation for the nonlinear Schrödinger equation.
Introduction to the method of complex scaling.
Solutions to Stein's Fourier analysis problems. (tex file)