Wilhelm Schlag
Department of Mathematics
University of Chicago
5734 South University Avenue
Chicago, IL 60637
Office phone: (773) 7027390
Fax: (773) 7029787
Email: schlag at math dot uchicago dot edu
Vita
Editorial boards
Recent papers

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
 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. Has appeared,
published by Cambridge University Press.
See here for the UK website Vol 1 and
Vol 2
A 20% discount can be obtained via this site
discount
Teaching

Notes from a course on Schrödinger equations
These are very rough lecture notes from an introductory class on linear and nonlinear Schrödinger equations.
Use with caution, they need a lot of work. I hope to revise them in the future.

Notes from a complex analysis class
Lecture notes from a first year graduate class at Chicago.
They are still incomplete and need more work. Comments and suggestions are welcome.
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
RTG Summer School 2014
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.