Wilhelm Schlag

About

Wilhelm Schlag is the Phillips Professor of Mathematics at Yale University. His research interests encompass a broad range of topics in mathematical analysis and differential equations. Specifically, he focuses on linear and nonlinear wave equations, investigating the stability of solitons and topological solitons. His work also includes spectral theory of differential operators and the distorted Fourier transform, as well as the spectral theory of lattice Schrödinger operators with quasiperiodic potentials. Additionally, Schlag engages in computer-assisted proofs in differential equations and spectral problems, and his expertise extends to classical and harmonic analysis. At Yale, he contributes to the academic community through teaching various courses in mathematics.

Research topics

• Quantum mechanics
• Combinatorics
• Pure mathematics
• Mathematics
• Mathematical analysis

Selected publications

• Asymptotic stability of the sine-Gordon kink under odd perturbations

  Duke Mathematical Journal · 2023-10-01 · 13 citations

  articleSenior author

  We establish the asymptotic stability of the sine-Gordon kink under odd perturbations that are sufficiently small in a weighted Sobolev norm. Our approach is perturbative and does not rely on the complete integrability of the sine-Gordon model. Key elements of our proof are a specific factorization property of the linearized operator around the sine-Gordon kink, a remarkable nonresonance property exhibited by the quadratic nonlinearity in the Klein–Gordon equation for the perturbation, and a var…

  PublisherDOI

• On Localization and the Spectrum of Multi-frequency Quasi-periodic Operators

  Vietnam Journal of Mathematics · 2023 · 13 citations

  PublisherOA PDFDOI

• On Modified Scattering for 1D Quadratic Klein–Gordon Equations With Non-Generic Potentials

  International Mathematics Research Notices · 2022-01-11 · 11 citations

  preprintOpen accessCorresponding

  Abstract We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein–Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to continue the investigation of the occurrence of a novel modified scattering behavior of the solutions that involves a logarithmic slow-down of the decay rate along certain rays. This phenomenon is ultimately caused by the threshold resonance of the lin…

  PublisherOA PDFDOI

• On codimension one stability of the soliton for the 1D focusing cubic Klein-Gordon equation

  Communications of the American Mathematical Society · 2024-02-28 · 9 citations

  articleOpen accessSenior author

  We consider the codimension one asymptotic stability problem for the soliton of the focusing cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to full asymptotic stability on the center-stable manifold is a small divisor in a quadratic source term of the perturbation equation. This singularity is due to the threshold resonance of the linearized operator and the absence of null structure in the nonlinearity. The threshold resonance of the linearized operator p…

  PublisherDOI

• An introduction to multiscale techniques in the theory of Anderson localization, Part I

  Nonlinear Analysis · 2022-03-15 · 9 citations

  article1st authorCorresponding
  PublisherDOI

Recent grants

• Harmonic Analysis with Applications to Mathematical Physics

  NSF · $85k · 2005–2007

• Long-Term Dynamics of Nonlinear Evolution Partial Differential Equations

  NSF · $375k · 2015–2018

• Harmonic Analysis, Mathematical Physics, and Nonlinear PDE

  NSF · $288k · 2007–2013

Frequent coauthors

• Joachim Krieger

  École Polytechnique Fédérale de Lausanne

  52 shared

• Carlos E. Kenig

  University of Chicago

  38 shared

• Andrew Lawrie

  30 shared

• Camil Muscalu

  Romanian Academy

  27 shared

• Baoping Liu

  State Grid Corporation of China (China)

  25 shared

• Kenji Nakanishi

  24 shared

• Roland Donninger

  University of Vienna

  20 shared

• Avy Soffer

  19 shared

Similar researchers at Yale University

• Ronald Coifmanh-74
• Vladimir Rokhlinh-60
• Dan Spielmanh-57