Wilhelm Schlag
Department of Mathematics
Yale University
10 Hillhouse
New Haven, CT 06520
Office phone: (203) 4324190
Fax: (203) 4327316
Email: wilhelm dot schlag dot yale dot edu
Vita
Editorial boards
Recent papers
 Weyl sums and the Lyapunov exponent for the skewshift Schrödinger cocycle
with Rui Han, Marius Lemm, preprint 2018.

A higher dimensional BourgainDyatlov fractal uncertainty principle
with Rui Han, preprint 2018.

Effective multiscale approach to the Schrödinger cocycle over a skew shift base
with Rui Han, Marius Lemm, preprint 2018.
 Intertwining wave operators, Fourier restriction, and Wiener theorems
W. Schlag, preprint 2018.
 Long time dynamics for weakly damped nonlinear KleinGordon equations
with Nicolas Burq, Genevieve Raugel, preprint 2018.

On the Spectrum of MultiFrequency Quasiperiodic Schrödinger Operators with Large Coupling
with Michael Goldstein, Mircea Voda, preprint 2017.
 Global center stable manifold for the defocusing energy critical wave equation with potential
with H. Jia, B. Liu, G. Xu, preprint 2017.
 Structure formulas for wave operators under a small scaling invariant condition
with M. Beceanu, preprint 2017.
 Structure formulas for wave operators
with M. Beceanu, preprint 2016.
 On localization and the spectrum of multifrequency quasiperiodic operators
with M. Goldstein, M. Voda, preprint 2016.
 Cartan Covers and Doubling Bernstein Type Inequalities on Analytic Subsets of C^2
with M. Goldstein, M. Voda, preprint 2016.
 Linear stability of the Skyrmion
with M. Creek, R. Donninger, S. Snelson, preprint 2016.
 The Weber equation as normal form with applications to top of the barrier scattering
with R. Costin, H. Park, preprint 2015.
 Generic and nongeneric behavior of solutions to the defocusing energy critical wave equation with potential in the radial case
with H. Jia, B. Liu, G. Xu, preprint 2015
 Long time dynamics for damped KleinGordon equations
with N. Burq, G. Raugel, preprint 2015
 Homogeneity of the spectrum for quasiperiodic Schroedinger operators
with D. Damanik, M. Goldstein, M. Voda, preprint 2015
 Stable soliton resolution for exterior wave maps in all equivariance classes
with C. Kenig, A. Lawrie, B. Liu, preprint 2014
 Channels of energy for the linear radial wave equation
with C. Kenig, A. Lawrie, B. Liu, preprint 2014
 Semilinear wave equations, ICM proceedings, Seoul Korea August 2014,
ICM14
 Large global solutions for energy supercritical nonlinear wave equations on R^{3+1}
with Joachim Krieger, preprint 2014
 Profiles for the radial focusing 4d energycritical wave equation
with R. Cote, C. Kenig, A. Lawrie, preprint 2014

Centerstable manifold of the ground state in the energy space for the critical wave equation
with Joachim Krieger and Kenji Nakanishi, preprint 2013

Relaxation of wave maps exterior to a ball to harmonic maps for all data
with Carlos Kenig, Andrew Lawrie, preprint 2013

Exotic blowup solutions for the u^5 focusing wave equation in R^3
with R. Donninger, M. Huang, J. Krieger, preprint 2012

Full range of blow up exponents for the quintic wave equation in three dimensions
with Joachim Krieger, preprint 2012

The method of concentration compactness and dispersive Hamiltonian evolution
equations.
Proceedings from the 2012 ICMP at Aalborg, Denmark.

Regularity and convergence rates for the Lyapunov exponents of linear cocycles
preprint 2012

Characterization of large energy solutions of the equivariant wave map problem: II
with Raphael Cote, Carlos Kenig, Andrew Lawrie, preprint 2012

Characterization of large energy solutions of the equivariant wave map problem: I
with Raphael Cote, Carlos Kenig, Andrew Lawrie, preprint 2012

Energy partition for the linear radial wave equation
with Raphael Cote, Carlos Kenig, preprint 2012

Threshold phenomenon for the quintic wave equation in three dimensions
with Joachim Krieger, Kenji Nakanishi, preprint 2012
More...
Slides from talks
 ICM talk
 Introduction, Lecture 1, Lecture 2, Lecture 3, Lecture 4
Anderson localization, small divisors, and subharmonic functions
Slides for the September 1521 2013 meeting at Maiori, Italy, and the minicourse in Vienna, Austria, 09/2527, 2013.
Many thanks to Michael Goldstein and Silvius Klein for helpful suggestions
which improved the presentation.

Concentration compactness and dispersive Hamiltonian equations
Slides from the ICMP at Aalborg, Denmark, August, and IMA, Minneapolis, September 2012

Decay of waves on a curved background
These are an extended form of slides used in various talks describing the dispersive decay of waves
on curved backgrounds with trapping. Examples are surfaces of revolution which are asymptotically conic, but also the
Schwarzschild black hole background.

Invariant manifolds for dispersive Hamiltonian evolution equations
These slides describe the global dynamics of solutions with energies near that of unstable ground state solitons for dispersive
certain Hamiltonian evolution equations.

Invariant manifolds and dispersive Hamiltonian evolution equations
This is an overview talk, delivered at the joint AMS/MAA meeting, Boston, January 5, 2012.
More...
Books

Concentration compactness for critical wave maps,
with Joachim Krieger.
This is our proof of global existence for large data
energy critical wave maps into
the hyperbolic plane based on the profile decomposition.
Has appeared in the series "Monographs" of the EMS Publishing house: EMS

Invariant Manifolds and dispersive Hamiltonian Evolution Equations,
with Kenji Nakanishi.
This is based on a course taught at ETH Zürich in
the fall of 2010.
Many thanks to Martin Sack at ETH for his help in preparing these lecture notes.
Has appeared in ''Zürich lectures in Advanced Mathematics'' of the EMS Publishing
House.
The link to the publisher page is here
EMS. In North America, the book can be ordered via the AMS, see
ORDER.
 Classical and Multilinear Harmonic Analysis, with Camil Muscalu.
The first volume of this book, which covers classical harmonic analysis, is a much
revised and expanded version of my old harmonic analysis notes, see below.
There is a completely new multilinear part as a second volume which covers Carleson's
theorem, the bilinear Hilbert transform and much more. To appear early 2013
with Cambridge University Press.
See here for Vol 1 and
Vol 2
Teaching
Meetings and Conferences
 PDE Conference in Ascona
This meeting brought together experts in completely integrable equations and KAM theory with those using more
harmonic analysis oriented methods. It took place in Ascona, Switzerland, July 16, 2012. It was organized by
Dario Bambusi, Thomas Kappeler, Joachim Krieger and myself.
 Joint AMS/MAA meeting, Boston
Together with
Eugene Wayne
from Boston University, I organized a special session on
"Stability Analysis for Infinite Dimensional Hamiltonian Systems" at the Joint Mathematics
Meeting that was held
Jan. 45, 2012 in Boston.
More information can be found here:
AMS
Numerical Data

Numerical results for radial nonlinear KleinGordon in three dimensions
Under this link the reader will find most of the numerical data as well as Ccodes
which were produced together with Roland Donninger in 2010 using a MacPro 8core work station.
These data can only be understood in conjunction with the paper 'Numerical study of the
blowup/global existence dichotomy etc.' which can be found above. Although the authors have
also
conducted computations on the
NICS CRAY XT5 supercomputer
which are described in this paper,
we have only deposited the MacPro material here as the CRAY uses MPI and is not so easily portable.
For the most part, the data are accompanied by readme files which offer some information about the codes.
The directory linked here is simply a copy of a (somewhat cleaned up) working directory which was used in the process of
producing the data. The executables were erased, as well as the .pdf files of the pictures which are simply too large.
All pictures are in .png format, and they were produced from the data files (.dat) via gnuplot.