Spectral theory for Schrödinger/Jacobi operators and Anderson localization, geometric function theory.

• (with M. Goldstein, W. Schlag) On the Spectrum of Multi-Frequency Quasiperiodic Schrödinger Operators with Large Coupling, ArXiv e-prints (2017), submitted, 68 pages, arXiv.
• (with M. Goldstein, W. Schlag) Cartan covers and doubling Bernstein type inequalities on analytic subsets of ℂ², ArXiv e-prints (2016), submitted, 18 pages, arXiv.
• (with M. Goldstein, W. Schlag) On localization and the spectrum of multi-frequency quasi-periodic operators, ArXiv e-prints (2016), submitted, 51 pages, arXiv.
• (with I. Binder, D. Kinzebulatov) Non-Perturbative Localization with Quasiperiodic Potential in Continuous Time, Comm. Math. Phys. 351 (2017), Issue 3, 1149-1175, arXiv, doi.
• (with D. Damanik, M. Goldstein, W. Schlag) Homogeneity of the spectrum for quasi-periodic Schrödinger operators, ArXiv e-prints (2015), accepted in J. Eur. Math. Soc. (JEMS), 35 pages, arXiv.
• (with K. Tao) Hölder continuity of the integrated density of states for quasi-periodic Jacobi operators, J. Spectr. Theory 7 (2017), no. 2, 361-386, arXiv, doi.
• (with I. Binder and M. Goldstein) On the Sum of the Non-Negative Lyapunov Exponents for Some Cocycles Related to the Anderson Model, Ergodic Theory and Dynamical Systems 37 (2017), Issue 2, 369-388, arXiv, doi.
• (with I. Binder and M. Goldstein) On fluctuations and localization length for the Anderson model on a strip, J. Spectr. Theory 5 (2015), no. 1, 193-225, arXiv, doi.
• (with I. Binder) On Optimal Separation of Eigenvalues for a Quasiperiodic Jacobi Matrix, Comm. Math. Phys. 325 (2014), Issue 3, 1063-1106, arXiv, doi.
• (with I. Binder) An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size n contained in an interval of size n^-C, J. Spectr. Theory 3 (2013), no. 1, 1-45, arXiv, doi.
• Solution of a Loewner chain equation in several complex variables, J. Math. Anal. Appl. 375 (2011), no. 1, 58--74, arXiv, doi.

• On Effective Localization Length for the Anderson Model on a Strip, Oberwolfach Reports, Report no. 36/2013, doi.
• Separation of Eigenvalues for Quasiperiodic Jacobi Matrices, Oberwolfach Reports, Report no. 36/2013, doi.
• Regularity of the Lyapunov exponent II,Oberwolfach Reports, Report no. 17/2012, doi.