Wilhelm Schlag

Department of Mathematics
University of Chicago
5734 South University Avenue
Chicago, IL 60637

Office phone: (773) 702-7390
Fax: (773) 702-9787
Email: schlag at math dot uchicago dot edu

Vita

• Curriculum vitae


• Bibliography

Editorial boards

• Geometric and Functional Analysis (GAFA)


• Transactions of the AMS


• Memoirs of the AMS


• Bulletin et Mémoires de la Societe Mathematique de France


• Journal of Spectral Theory


• Analysis and PDE


• Communications Math Physics (CMP)

Recent papers

1. Center-stable manifold of the ground state in the energy space for the critical wave equation
   with Joachim Krieger and Kenji Nakanishi, preprint 2013


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


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


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


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


6. Regularity and convergence rates for the Lyapunov exponents of linear co-cycles
   preprint 2012


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


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


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


10. Threshold phenomenon for the quintic wave equation in three dimensions
    with Joachim Krieger, Kenji Nakanishi, preprint 2012

More...

Slides from talks

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


2. 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.


3. 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.


4. 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

• Harmonic analysis notes.
  These are my old harmonic analysis notes, see the book announcement above.


• 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 1-6, 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. 4-5, 2012 in Boston.
More information can be found here: AMS

Numerical Data

• Numerical results for radial nonlinear Klein-Gordon in three dimensions
  Under this link the reader will find most of the numerical data as well as C-codes
  which were produced together with Roland Donninger in 2010 using a MacPro 8-core 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.