Welcome Short CV Research Publications Teaching

You can find my preprints on the ArXiv here. Here is some recent work.

  1. (with Camille Schuetz) Solutions to the fifth-order KPII equation scatter. ArXiV

Here are some representative papers from 1981 to the present.

  1. (with Israel Sigal, Barry Simon): Spectral Analysis of N-body Schrödinger operators. Ann. of Math. (2) 114 (1981), 519–567.

  2. (with Robert Brooks, Paul Yang): Isospectral sets of conformally equivalent metrics. Duke Math. J. 58 (1989), no. 1, 131–150.

  3. (with Robert Brooks, Peter Petersen): Spectral geometry in dimension 3. Acta Math. 173 (1994), no. 2, 283–305.

  4. (with Desmond Evans, Heinz Siedentop) The spectrum of relativistic one-electron atoms according to Bethe and Salpeter. Comm. Math. Phys. 178 (1996), no. 3, 733–746.

  5. (with S. J. Patterson) The divisor of Selberg's zeta function for Kleinian groups. Appendix A by Charles Epstein. Duke Math. J. 106 (2001), no. 2, 321–390.

  6. A Poisson summation formula and lower bounds for resonances in hyperbolic manifolds. Int. Math. Res. Not. IMRN. 2003, no. 34, 1837–1851.

  7. (with Thomas Kappeler, Mikhail Shubin, Peter Topalov) The Miura map on the line. Int. Math. Res. Not. IMRN 2005, no. 50, 3091–3133. ArXiV

  8. (with David Borthwick, Tanya Christiansen, Peter Hislop) Resonances for manifolds hyperbolic near infinity: optimal lower bounds on order of growth. Int. Math. Res. Not. IMRN 2011, no. 19, 4431–4470. ArXiV

  9. (with Richard Ehrenborg, Sergei Kitaev) A spectral approach to consecutive pattern-avoiding permutations. J. Comb. 2 (2011), no. 3, 305–353. ArXiV

  10. Global well-posedness and long-time asymptotics for the defocussing Davey-Stewartson II equation in H1,1(ℂ). With an appendix by Michael Christ. J. Spectr. Theory 6 (2016), no. 3, 429–481. ArXiV

  11. (with Russell Brown and Katharine Ott) Action of a scattering map on weighted Sobolev spaces in the plane. J. Funct. Anal. 271 (2016), no. 1, 85–106. ArXiV

  12. (with Robert Jenkins, Jiaqi Liu, and Catherine Sulem) Soliton resolution for the derivative nonlinear Schrödinger equation. Comm. Math. Phys. 363 (2018), no. 3, 1003–1049. ArXiV

  13. Inverse scattering and well-posedness in one and two dimensions. Nonlinear dispersive partial differential equations and inverse scattering, 161–252. Fields Inst. Commun., 83. Springer, New York, 2019. ArXiV

  14. (with Robert Jenkins, Jiaqi Liu, and Catherine Sulem) Global existence for the derivative nonlinear Schröodinger equation with arbitrary spectral singularities. Anal. PDE 13 (2020), no.5, 1539–1578 ArXiV