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.

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. Scattering for defocusing energy subcritical nonlinear wave equations. (with with B. Dodson, D. Mendelson, and J. Murphy);
    preprint 2018.

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

  3. 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

  4. Conditional stable soliton resolution for a semi-linear Skyrme equation (with C. Rodriguez);
    preprint 2017.

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

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

  12. 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.

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

  14. 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.

  15. 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.

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

  17. 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.

  18. 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.

  19. 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.

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

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

Seminars

Teaching


Thesis and Expository Notes