Andrew Lawrie


I am an Assistant Professor of Mathematics at MIT. Previously, I was an NSF postdoc at UC Berkeley. I did my PhD in Mathematics at the University of Chicago. My advisor was Prof. Wilhelm Schlag. My research is supported in part by the NSF and the Sloan Foundation.

Contact Information

Department of Mathematics
Massachusetts Institute of Technology
2-267
Cambridge, MA 02139

Email: alawrie at mit dot edu

Vita:


Papers and Preprints

The following are all available on my arXiv.org page.
  1. Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line. (with J. Jendrej and M. Kowalczyk);
    preprint 2019.

  2. Asymptotic stability of harmonic maps on the hyperbolic plane under the Schrödinger maps evolution. (with J. Luhrmann, S.-J. Oh and S. Shahshahani); preprint 2019.

  3. Dynamics of bubbling wave maps with prescribed radiation. (with with J. Jendrej and C. Rodriguez);
    preprint 2019.

  4. Scattering for defocusing energy subcritical nonlinear wave equations. (with with B. Dodson, D. Mendelson, and J. Murphy);
    Analysis and PDE, to appear.

  5. Local smoothing estimates for Schrodinger equations on hyperbolic space. (with J. Luhrmann, S.-J. Oh and S. Shahshahani);
    preprint 2018.

  6. Two bubble dynamics for threshold solutions to the wave maps equation (with J. Jendrej);
    Invent. Math. 213 (2018) no. 3, 1249-1325 link to online version

  7. Conditional stable soliton resolution for a semi-linear Skyrme equation (with C. Rodriguez);
    Annals of PDE, to appear.

  8. The Cauchy problem for wave maps on hyperbolic space in dimensions d ≥ 4. (with S.-J. Oh and S. Shahshahani);
    IMRN Vol. 2018, No. 7, 1954-2051

  9. Equivariant wave maps on the hyperbolic plane with large energy (with S.-J. Oh and S. Shahshahani);
    Math. Res. Lett. 24 (2017) no. 2, 449-479

  10. A refined threshold theorem for (1+2)-dimensional wave maps into surfaces (with S.-J. Oh);
    Comm. Math. Phys. 342 (2016) no. 3, 989-999.

  11. Gap eigenvalues and asymptotic dynamics of geometric wave equations on hyperbolic space (with S.-J. Oh and S. Shahshahani);
    J. Funct. Anal. 271 (2016), no. 11, 3111-3161.

  12. Profile decompositions for wave equations on hyperbolic space with applications (with S.-J. Oh and S. Shahshahani);
    Math. Ann. 365 (2016), no. 1-2, 707-803.

  13. Stable soliton resolution for exterior wave maps in all equivariance classes. (with C. Kenig, B. Liu, and W. Schlag);
    Advances in Math. 285 (2015), 235-300.

  14. Channels of energy for the linear radial wave equation. (with C. Kenig, B. Liu, and W. Schlag);
    Advances in Math. 285 (2015), 877-936.

  15. Scattering for radial, semi-linear, super-critical wave equations with bounded critical norm. (with B. Dodson);
    Arch. Rational Mech. and Anal. 218 (2015) no. 3, 1459-1529.

  16. Scattering for the radial 3d cubic wave equation. (with B. Dodson);
    Analysis and PDE. 8 (2015) no. 2, 467-497.

  17. Stability of stationary equivariant wave maps from the hyperbolic plane. (with S.-J. Oh and S. Shahshahani);
    Amer. J. Math. 139 (2017) no. 4, 1085-1147.

  18. Profiles for the radial focusing 4d energy-critical wave equation. (with R. Cote, C. Kenig, and W. Schlag);
    Comm. Math. Phys. 357 (2018), no. 3, 943--1008.

  19. Conditional global existence and scattering for a semi-linear Skyrme equation with large data.
    Comm. Math. Phys.. 334 (2015) no. 2, 1025-1081.

  20. Relaxation of wave maps exterior to a ball to harmonic maps for all data. (with C. Kenig and W. Schlag);
    Geom. Funct. Anal. (GAFA). 24 (2014), no. 2, 610-647.

  21. Characterization of large energy solutions of the equivariant wave maps problem: I. (with R. Cote, C. Kenig, and W. Schlag);
    Amer. J. Math. 137 (2015) no. 1, 139-207.

  22. Characterization of large energy solutions of the equivariant wave maps problem: II. (with R. Cote, C. Kenig, and W. Schlag);
    Amer. J. Math. 137 (2015) no. 1, 209-250.

  23. Scattering for wave maps exterior to a ball. (with W. Schlag);
    Advances in Math. 232 (2013), no. 1, 57-97.

  24. The Cauchy problem for wave maps on a curved background.
    Calc. Var. Partial Differential Equations. 45 (2012), no. 3-4, 505-548.

Seminars

Thesis and Expository Notes