Interests:
I currently enjoy thinking about spectral theory of discrete one-dimensional Schrödinger operators, particularly those whose potentials are generated by infinite-measure ergodic dynamical systems.

Publications:

• Continuum Schrödinger operators associated with aperiodic subshifts, with David Damanik and Anton Gorodetski (submitted)
• Dynamics of unitary operators, with David Damanik and Robert Vance (in preparation)
• Ergodic Schrödinger operators in the infinite measure setting, with Michael Boshernitzan, David Damanik, and Milivoje Lukic (in preparation)

Talks:

• "The Kunz-Souillard Approach to Localization II" Rice University, (January 22, 2013)
• "Basic Spectral Theory" Rice University, (January 17, 2013)
• "The Kunz-Souillard Approach to Localization I" Rice University, (January 8, 2013)
• "Progress Towards the Almost Reducibility Conjecture," MFO, Oberwolfach, Germany (April 6, 2012)
  
• "Schrödinger Operators with Sparse Potentials," Rice University (February 8, 2012)
  
• "Real Floquet Theory of Periodic Jacobi Matrices," Rice University (January 20, 2012)
  
• "Periodic Jacobi Matrices: The 'Magic' Formula," Rice University (November 16, 2011)
  
• "Generalized Eigenfunctions and Spectra," Rice University (September 14, 2011
  
  

Conferences:

• 31st Annual Western States Mathematical Physics Meeting, California Institute of Technology, Pasadena, CA, USA (February 18-19, 2013) webpage
  
• Recent Advances in Harmonic Analysis and Spectral Theory, Texas A&M University, College Station, TX (August 6-10, 2012). webpage
  
• Arbeitsgemeinschaft on Quasiperiodic Schrödinger Operators, MFO, Oberwolfach, Germany (April 1-7, 2012). webpage
  
• 30th Annual Western States Mathematical Physics Meeting, California Institute of Technology, Pasadena, CA (February 20-21, 2012). webpage
  
• Ahlfors-Bers Colloquium, Rice University, Houston, TX (March 24-27, 2011). webpage