Michael VanValkenburgh

Contact Information:

Teaching:

Curriculum Vitae.

Publications:

• Manipulation of Semiclassical Photon States. J. Math. Phys. 50, 023501 (2009).
• Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators. Math. Res. Lett. 16 (2009), no. 4, 721-–734.
• Laguerre-Gaussian Modes and the Wigner Transform. Journal of Modern Optics. Volume 55, Issue 21, 3535--3547 (2008).
• Dissertation. (last updated: 5/21/09)
  (pdf)

Research Notes:

• Unique Continuation for J-holomorphic Curves. (This is a special case of a proof from [Hormander III].)
• Manipulation of Semiclassical Laguerre-Gaussian Modes: a Model Case. In my dissertation.
• Exponential Lower Bounds for the Bargmann Transform. In my dissertation.
• The Pseudospectrum of Zakharov-Shabat.
  (pdf)

Expository Notes:

• Notes on a Paper of Shiffman and Zelditch
  (pdf)
• Notes on Calderón's Problem
  (pdf)
• A Fun Linear Algebra Problem
  (pdf)
• Wherefore Cotangent Space?
  (pdf)
• Parental Advisory.
  (pdf)
• Iagolnitzer's Microlocal Upper Bounds.
  (pdf)

(Unauthorized) Translations:

• Classification of Integrable Systems in Dimension 2, by Dufour, Molino, and Toulet (pdf).
  
• Sjöstrand's monograph Singularités Analytiques Microlocales (pdf). (last updated: 7/21/09)
  Corrections (pdf). (last updated: 8/11/09)
  Commentary (pdf). (last updated: 8/5/09)

Miscellany: