Kiril Datchev
CLE Moore Instructor and NSF Postdoctoral Fellow
Department of Mathematics
Massachusetts Institute of Technology
Mentor: Richard Melrose
Office: Building 2, Room 173
Email: datchev@math.mit.edu

Teaching

In Fall 2012 I taught 18.100B Real Analysis.
In Spring 2013 I am teaching 18.104 Seminar in Analysis.

Research Interests

Partial differential equations, mathematical physics. Geometric scattering theory and inverse problems, nonlinear evolution equations.
Research Papers
  1. Asymptotic distribution of phase-shifts: spherical symmetry, with Jesse Gell-Redman, Andrew Hassell, and Peter Humphries.

  2. Resonance free regions for nontrapping manifolds with cusps.

  3. Sharp polynomial bounds on the number of Pollicott-Ruelle resonances, with Semyon Dyatlov and Maciej Zworski. To appear in Ergodic Theory and Dynamical Systems.

  4. Fractal Weyl laws for asymptotically hyperbolic manifolds, with Semyon Dyatlov. To appear in Geometric and Functional Analysis.

  5. Semiclassical resolvent estimates at trapped sets, with András Vasy. To appear in Annales de l'Institut Fourier.

  6. Extending cutoff resolvent estimates via propagation of singularities. Communications in Partial Differential Equations, Vol. 37, No. 8, pp. 1456–1461, 2012.

  7. Resonant uniqueness of radial semiclassical Schrödinger operators, with Hamid Hezari. Applied Mathematics Research Express, Vol. 2012, No. 1, pp. 105–113, 2012.

  8. Spectral uniqueness of radial semiclassical Schrödinger operators, with Hamid Hezari and Ivan Ventura. Mathematical Research Letters, Vol. 18, No. 3, pp. 521–529, 2011.

  9. Propagation through trapped sets and semiclassical resolvent estimates, with András Vasy. To appear in Annales de l'Institut Fourier. See also a short report on the result.

  10. Gluing semiclassical resolvent estimates via propagation of singularities, with András Vasy. International Mathematics Research Notics, Vol. 2012, No. 23, pp. 5409–5443, 2012. See also my coauthor's short report on the result.

  11. Solitary waves for the Hartree equation with a slowly varying potential, with Ivan Ventura. Pacific Journal of Mathematics, Vol. 248, No. 1, pp. 63–90, 2010.

  12. Fast soliton scattering by attractive delta impurities, with Justin Holmer. Communications in Partial Differential Equations, Vol. 34, No. 9, pp. 1074–1113, 2009.

  13. Local smoothing for scattering manifolds with hyperbolic trapped sets. Communications in Mathematical Physics, Vol. 286, No. 3, pp. 837–850, 2009.

Expository Papers
  1. Inverse problems in spectral geometry, with Hamid Hezari. Inverse Problems and Applications: Inside Out II. Mathematical Sciences Research Institute Publications, No. 60, pp. 455--486, 2012.

  2. Introduction to the method of complex scaling, 2006.
PhD Thesis
Distribution of resonances for manifolds with hyperbolic ends, May 2010. My thesis advisor was Maciej Zworski.