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


• Transactions of the AMS


• Memoirs of the AMS


• Bulletin et Mémoires de la SMF


• Journal of Spectral Theory


• Analysis and PDE

Recent papers

1. Global dynamics of the nonradial energy-critical wave equation above the ground state energy
   with Joachim Krieger, Kenji Nakanishi, preprint 2011


2. Scattering for wave maps exterior to a ball
   with Andrew Lawrie, preprint 2011


3. On the spectral properties of L_{+-} in three dimensions
   with Ovidiu Costin, Min Huang, to appear in Nonlinearity.


4. Semiclassical low energy scattering for one--dimensional Schroedinger operators with exponentially decaying potentials
   with Ovidiu Costin, Roland Donninger, and Saleh Tanveer, to appear in Annales Henri Poincare


5. Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation with Kenji Nakanishi,
   to appear in SIAM Journal of Analysis


6. Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation with Roland Donninger,
   Nonlinearity 24 (2011) 2547-2562.


7. Global dynamics above the ground state energy for the one-dimensional NLKG equation with Joachim Krieger and Kenji Nakanishi,
   to appear in Math. Z.


8. Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption with Kenji Nakanishi,
   to appear in Arch. Rat. Mechanics and Analysis


9. Global dynamics away from the ground state for the energy-critical nonlinear wave equation with Joachim Krieger and Kenji Nakanishi,
   to appear in Amer. Journal of Math.

More...

Slides from talks

1. 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.


2. 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.


3. 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, preprint 2009.
  This is our proof of global existence for large data energy critical wave maps into
  the hyperbolic plane based on the profile decomposition.
  To appear in the series "Monographs" of the EMS Publishing house in early 2012.


• 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.
  To appear 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.


• Linear and Multilinear Harmonic Analysis, with Camil Muscalu.
  The first half of this book, which covers classical harmonic analysis, is going to contain
  a revised and expanded version of my old harmonic analysis notes. A first revision can be found here, but the one
  which will be in the book is going to be longer and more extensive.
  There will be a completely new multilinear part written by Camil which will cover Carleson's
  theorem, the bilinear Hilbert transform and much more. Should appear early 2013
  with Cambridge University Press.

Teaching

• Harmonic analysis notes.
  These are my old harmonic analysis notes. They are currently being reworked, see the book
  announcement above for an updated version.


• 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
  These are lecture notes from a first year graduate class at Chicago.
  They are still incomplete and need more work. Comments and suggestions are welcome.
  These may also become a book at some point.

Meetings and Conferences

• PDE Conference in Ascona
This meeting brings together experts in completely integrable equations and KAM theory with those using more
harmonic analysis oriented methods. It will take place in Ascona, Switzerland, July 1-6. It is being organized by
Dario Bambusi, Thomas Kappeler, Joachim Krieger and myself.


• Joint AMS/MAA meeting, Boston
Together with Eugene Wayne from Boston University, I am organizing a special session on
"Stability Analysis for Infinite Dimensional Hamiltonian Systems" at the Joint Mathematics Meetings to be held
Jan. 4-5, 2012 in Boston (the meeting will be 4-7 but the special session takes place on Jan. 4,5).
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.