About

Jared Wunsch received his PhD from Harvard University in 1998. After completing a postdoctoral position at Columbia University and a faculty position at Stony Brook University, he joined Northwestern University in 2002. Wunsch works in the fields of microlocal analysis and spectral and scattering theory. Much of his work concerns how the behavior of waves is influenced by the geometry of the space on which they propagate, especially when that geometry is allowed to be singular. He served as chair of the mathematics department from 2012 to 2015. Wunsch was named a Fellow of the American Mathematical Society in 2013 and was awarded a Simons Fellowship in 2021. In recognition of his teaching, he received a WCAS Distinguished Teaching Award in 2011.

Research topics

• Physics
• Quantum mechanics
• Mathematics
• Mathematical analysis
• Geometry
• Mathematical physics
• Quantum electrodynamics

Selected publications

• On the convergence of the Born series for Coulomb potentials

  ArXiv.org · 2025-12-18

  articleOpen accessSenior author

  We provide a short proof of the convergence of the Born series on asymptotically conic manifolds, at sufficiently high energy. The potential is allowed to have multiple Coulomb singularities. This is handled using powerful semiclassical estimates recently proven by Hintz for the case of a single dipole (or better) singularity. The potential is also allowed to be long-range, like the actual Coulomb potential $1/r$; long-range potentials are handled using anisotropic semiclassical (sc-) Sobolev spaces. As a consequence of the above estimates, we show the existence of a resonance-free region for Hamiltonians with multiple screened Coulomb singularities.

  PublisherOA PDF

• Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed

  Journal of Differential Equations · 2025-05-27

  articleOpen access

  We consider Helmholtz problems with a perturbed wave speed, where the single-signed perturbation is linear in a parameter z . Both the wave speed and the perturbation are allowed to be discontinuous (modelling a penetrable obstacle). We show that there exists a polynomial function of frequency such that, for any frequency, for most values of z , the norm of the solution operator is bounded by that function. This solution-operator bound is most interesting for Helmholtz problems with strong trapping; recall that here there exists a sequence of real frequencies, tending to infinity, through which the solution operator grows superalgebraically, with these frequencies often called quasi-resonances . The result of this paper then shows that, at every fixed frequency in the quasi-resonance, the norm of the solution operator becomes much smaller for most single-signed perturbations of the wave speed, i.e., quasi-resonances are unstable under most such perturbations.

  PublisherDOI

• A Gutzwiller trace formula for singular potentials

  ArXiv.org · 2025-09-05

  preprintOpen access1st authorCorresponding

  The Gutzwiller trace formula relates the asymptotic spacing of quantum-mechanical energy levels in the semiclassical limit to the dynamics of periodic classical particle trajectories. We generalize this result to the case of non-smooth potentials, for which there is partial reflection of energy from derivative discontinuities of the potential. It is the periodic trajectories of an associated branching dynamics that contribute to the trace asymptotics in this more general setting; we obtain a precise description of their contribution.

  PublisherOA PDFDOI

• Singularities of Dirac-Coulomb propagators

  ArXiv.org · 2025-07-21

  preprintOpen accessSenior author

  In this paper we study singularities of propagators and $N$-point functions for Dirac fields in a Coulomb potential, possibly with a $t$-dependent smooth part for $|t|

  PublisherOA PDFDOI

• On the convergence of the Born series for Coulomb potentials

  arXiv (Cornell University) · 2025-12-18

  preprintOpen accessSenior author

  We provide a short proof of the convergence of the Born series on asymptotically conic manifolds, at sufficiently high energy. The potential is allowed to have multiple Coulomb singularities. This is handled using powerful semiclassical estimates recently proven by Hintz for the case of a single dipole (or better) singularity. The potential is also allowed to be long-range, like the actual Coulomb potential $1/r$; long-range potentials are handled using anisotropic semiclassical (sc-) Sobolev spaces. As a consequence of the above estimates, we show the existence of a resonance-free region for Hamiltonians with multiple screened Coulomb singularities.

  PublisherDOI

• Propagation for Schrödinger Operators with Potentials Singular Along a Hypersurface

  Archive for Rational Mechanics and Analysis · 2024-04-14 · 1 citations

  articleOpen accessSenior author

  Abstract In this article, we study the propagation of defect measures for Schrödinger operators $$-h^2\Delta _g+V$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msub> <mml:mi>Δ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> on a Riemannian manifold ( M , g ) of dimension n with V having conormal singularities along a hypersurface Y in the sense that derivatives along vector fields tangential to Y preserve the regularity of V . We show that the standard propagation theorem holds for bicharacteristics travelling transversally to the surface Y whenever the potential is absolutely continuous. Furthermore, even when bicharacteristics are tangential to Y at exactly first order, as long as the potential has an absolutely continuous first derivative, standard propagation continues to hold.

  PublisherOA PDFDOI

• The $hp$-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect

  Communications in Mathematical Sciences · 2024-01-01 · 11 citations

  articleOpen accessSenior author

  International audience

  PublisherOA PDFDOI

• Internal waves in a 2D subcritical channel

  arXiv (Cornell University) · 2024-11-21

  preprintOpen accessSenior author

  We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to outgoing data; this operator turns out to differ by a smoothing operator from the pullback by the ``bounce map'' for boundary data obtained by ray-tracing. As a consequence we obtain unique solvability of the inhomogeneous stationary scattering problem subject to an appropriate outgoing radiation condition.

  PublisherOA PDFDOI

• Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed

  arXiv (Cornell University) · 2024-02-01

  preprintOpen access

  We consider Helmholtz problems with a perturbed wave speed, where the single-signed perturbation is linear in a parameter $z$. Both the wave speed and the perturbation are allowed to be discontinuous (modelling a penetrable obstacle). We show that there exists a polynomial function of frequency such that, for any frequency, for most values of $z$, the norm of the solution operator is bounded by that function. This solution-operator bound is most interesting for Helmholtz problems with strong trapping; recall that here there exists a sequence of real frequencies, tending to infinity, through which the solution operator grows superalgebraically, with these frequencies often called $\textit{quasi-resonances}$. The result of this paper then shows that, at every fixed frequency in the quasi-resonance, the norm of the solution operator becomes much smaller for most single-signed perturbations of the wave speed, i.e., quasi-resonances are unstable under most such perturbations.

  PublisherOA PDFDOI

• Wave Propagation on Rotating Cosmic String Spacetimes

  Communications in Mathematical Physics · 2024-02-23

  article1st author
  PublisherDOI

Recent grants

• Linear Partial Differential Equations on Singular Spaces

  NSF · $72k · 2004–2007

• Linear Partial Differential Equations on Singular Spaces

  NSF · $195k · 2013–2017

• Linear Partial Differential Equations on Singular Spaces

  NSF · $180k · 2016–2019

• Linear Partial Differential Equations on Singular Spaces

  NSF · $270k · 2021–2025

• Linear Partial Differential Equations on Singular Spaces

  NSF · $198k · 2010–2013

Frequent coauthors

• András Vasy

  Stanford University

  35 shared

• Euan A. Spence

  University of Bath

  22 shared

• Dean Baskin

  20 shared

• Andrew Hassell

  16 shared

• David Lafontaine

  Institut de Mathématiques de Toulouse

  12 shared

• Jeffrey Galkowski

  University College London

  11 shared

• Richard Melrose

  10 shared

• D. Lafontaine

  Université de Toulouse

  10 shared

Labs

• RTG Dynamics: Classical, Modern and QuantumPI

Education

• Ph.D., Mathematics

  Massachusetts Institute of Technology

  1995

• B.S., Mathematics

  Harvard University

  1990

Awards & honors

• Fellow of the American Mathematical Society (2013)
• Simons Fellowship (2021)
• WCAS Distinguished Teaching Award (2011)