You can find my preprints on the ArXiv here. Here is some recent work.
- (with George Lytle) Nachman's reconstruction for the Calderon problem with discontinuous conductivities. ArXiV
- (with Robert Jenkins, Jiaqi Liu, Catherine Sulem) Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities. ArXiV
Here are some representative papers from 1981 to the present.
- (with Israel Sigal, Barry Simon): Spectral Analysis of N-body Schrödinger operators. Ann. of Math. (2) 114 (1981), 519–567.
- (with Robert Brooks, Paul Yang): Isospectral sets of conformally equivalent metrics.
Duke Math. J. 58 (1989), no. 1, 131–150.
- (with Robert Brooks, Peter Petersen): Spectral geometry in dimension 3.
Acta Math. 173 (1994), no. 2, 283–305.
- (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.
- (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.
- A Poisson summation formula and lower bounds for resonances in hyperbolic manifolds.
Int. Math. Res. Not. 2003, no. 34, 1837–1851.
- (with Thomas Kappeler, Mikhail Shubin, Peter Topalov) The Miura map on the line. Int. Math. Res. Not. 2005, no. 50, 3091–3133. ArXiV
- (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
- (with Richard Ehrenborg, Sergei Kitaev) A spectral approach to consecutive pattern-avoiding permutations. J. Comb. 2 (2011), no. 3, 305–353.
- 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
- (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
- (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