CV

Analysis / PDE Seminar

Research Publications / Preprints:

Most of my preprints / publications are available from the ArXiv.

• (with J. Marzuola and D. Tataru)  Quasilinear Schrödinger equations I: Small data and quadratic interactions.  Submitted, 2011.  (arXiv: 1106.0490)
• (with D. Tataru, and M. Tohaneanu)  Price's law on nonstationary spacetimes.  Submitted, 2011.  (arXiv: 1104.5437)
• (with M. Taylor)  Dispersive wave estimates on 3D hyperbolic space.  Proc. Amer. Math. Soc., to appear.
• (with J. Perry)  Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions.  Commun. Pure Appl. Anal., to appear.
  
• (with P. Laul)  Localized energy estimates for wave equations on high dimensional Schwarzschild space-times.  Proc. Amer. Math. Soc., to appear.  (arXiv: 1008.4626)
  
• (with C.D. Sogge)  Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles.  Discrete Contin. Dyn. Sys. 28 (2010), 1589--1601.  (arXiv: 0910.0433)
• (with M. Taylor)  Nonlinear waves on 3D hyperbolic space.  Trans. Amer. Math. Soc. 363 (2011), 3489--3529.
  
• (with D. Tataru)  Decay estimates for variable coefficient wave equations in exterior domains.  Advances in Phase Space Analysis of Partial Differential Equations, In Honor of Ferruccio Colombini's 60th Birthday.  Progress in Nonlinear Differential Equations and Their Applications, Vol. 78, 2009.  p. 201--217.  (arXiv: 0806.3409)
• (with K. Hidano, H. Smith, C.D. Sogge, and Y. Zhou)  On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles.  Trans. Amer. Math. Soc. 362 (2010), 2789--2809.  (arXiv: 0805.1673)
• (with J. Marzuola, D. Tataru, and M. Tohaneanu)  Strichartz estimates on Schwarzschild black hole backgrounds.  Comm. Math. Phys. 293 (2010), 37--83.  (arXiv: 0802.3942)
  
• (with Y. Du, C.D. Sogge, and Y. Zhou)  Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions. Comm. Partial Differential Equations 33 (2008), 1487--1506.  (arXiv: 0710.2026)
• (with D. Tataru)  Global parametrices and dispersive estimates for variable coefficient wave equations.  Math. Ann., to appear.  (arXiv: 0707.1191)
  
• (with J. Marzuola and D. Tataru)  Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations.  J. Funct. Anal. 255 (2008), 1497--1553.  (arXiv: 0706.0544)
  
• (with J. Marzuola and D. Tataru)  Wave packet parametrices for evolutions governed by PDO's with rough symbols.  Proc. Amer. Math. Soc. 136 (2008), 597--604.   (arXiv:  math/0611252)
• (with M. Nakamura) General quasilinear wave equations with localized dissipation in exterior domains.  J. Differential Equations  233 (2007), 313--344. 
  
• (with B. Thomases)  Elastic waves in exterior domains, Part II: Global existence with a null structure.  Int. Math. Res. Not.  2007, 1--43.   (arXiv:  math/0605110)
  
• Elastic waves in exterior domains, Part I: Almost global existence.  Int. Math. Res. Not.  2006, 1--41.
  
• (with C.D. Sogge)  Global existence of null-form wave equations in exterior domains.  Math. Z.  256 (2007), 521--549.   (arXiv:  math/0611489)
• (with A. Stewart)  Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions.   Trans. Amer. Math. Soc.   360 (2008), 171--188. (arXiv:  math/0509326)
  
• (with C.D. Sogge) Long time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods.  SIAM J. Math. Anal. 38 (2006), 188--209. 
  
• (with M. Lacey)  Paraproducts in one and several parameters.  Forum Math 19 (2007), 325--351.   (arXiv:  math/0502334)
• (with M. Nakamura and C.D. Sogge)  Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition.  Japan. J. Math.   31 (2005), 391--472.  (arXiv:  math/0409363)
  
• (with C.D. Sogge and A. Stewart) Nonlinear hyperbolic equations in infinite homogeneous waveguides.  Comm. Partial Differential Equations 30 (2005), 643--661.   (arXiv:  math/0411513)  
• (with C.D. Sogge) Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions.   Math. Ann. 336 (2006), 391--420.   (arXiv:  math/0404420)
• (with M. Nakamura and C.D. Sogge) Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains. Forum Math.  17 (2005), 133--168.    (arXiv:  math/0409362)
• (with C.D. Sogge) Hyperbolic trapped rays and global existence of quasilinear wave equations. Invent. Math.  159 (2005), 75--117.   (arXiv:  math/0301290)
•  Global existence for semilinear wave equations exterior to nontrapping obstacles.  Houston J. Math.  30 (2004), 259--281.  (arXiv:  math/0210246)
• Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle.  Trans. Amer. Math. Soc.  356 (2004), 4839--4855.   (arXiv:  math/0210227)

Thesis:  Global Strichartz Estimates for Solutions to the Wave Equation Exterior to a Convex Obstacle.  Johns Hopkins University, May 2003.  Advisor:  Christopher D. Sogge.

Extended Abstracts:

Slides:

Dispersive estimates for wave equations on black hole backgrounds
Price's law on nonstationary space-times
Localized energy estimates on high dimensional Schwarzschild blackhole backgrounds
Long time existence for quasilinear wave equations in exterior domains
Strichartz estimates for the wave equation on 3D hyperbolic space
Abstract Strichartz estimates and the Strauss conjecture for the wave equation in exterior domains
Nonlinear Hyperbolic Equations in Infinite Homogeneous Waveguides
On Keel-Smith-Sogge Estimates and Quasilinear Wave Equations in Exterior Domains
Quasilinear Wave Equations in Exterior Domains
Elastic Waves in Exterior Domains
A Multiplier Approach to KSS Estimates and Applications
Nonlinear Hyperbolic Equations in Waveguides
Global Existence of Solutions to Multiple Speed Systems of Quasilinear Wave Equations in Exterior Domains
Global Strichartz Estimates for Solutions of the Wave Equation in Exterior Domains
The Mathematics Behind JPEG
A Survey of Existence Results for Nonlinear Wave Equations in Exterior Domains

Education:

JOHNS HOPKINS UNIVERSITY, Ph.D. Mathematics, May 2003
UNIVERSITY OF WASHINGTON, B.S. Mathematics with distinction, June 1998
UNIVERSITY OF WASHINGTON, B.S. Computer Science, June 1998

Employment:

• July 2007 - present:  Assistant Professor, Department of Mathematics, University of North Carolina, Chapel Hill
  
• July 2006 - August 2007: NSF Postdoctoral Instructor / Charles B. Morray Assistant Professor, Department of Mathematics, University of California, Berkeley
• August 2005 - July 2006:  NSF Postdoctoral Fellow, Department of Mathematics, University of California, Berkeley
• Fall 2005:  Visiting Postdoctoral Member, MSRI
• August 2003 - August 2005:  VIGRE Visiting Assistant Professor, School of Mathematics, Georgia Institute of Technology