CV - (dvi, pdf)

Analysis / PDE Seminar

Carolina Meeting on Harmonic Analysis and PDE - January 30 - February 1, 2009

Research Publications / Preprints:

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

• (with C.D. Sogge)  Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles.  Submitted, 2009.  (arXiv: 0910.0433)
• (with M. Taylor)  Nonlinear waves on 3D hyperbolic space.  Trans. Amer. Math. Soc., to appear.
• (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., to appear.  (arXiv: 0805.1673)
• (with J. Marzuola, D. Tataru, and M. Tohaneanu)  Strichartz estimates on Schwarzschild black hole backgrounds.  Comm. Math. Phys., to appear.  (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:

Talks and Slides:

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

• Partial Differential Equations Seminar, Mathematisches Institut, Universität Bonn, Bonn, Germany, July 2009
  
• AMS 2009 Spring Western Section Meeting, Special Session on Nonlinear Partial Differential Equations, San Francisco, CA, April 2009
• AMS 2009 Spring Western Section Meeting, Special Session on Nonlinear Dispersive Equations, San Francisco, CA, April 2009
  
• Calderon-Zygmund Analysis Seminar, University of Chicago, Department of Mathematics, March 2009
  
• GMA Visions Seminar (with J. Hawkins on academic job searches), University of North Carolina, Department of Mathematics, October 2008
• Applied Math/Analysis Seminar, Duke University, Department of Mathematics, September 2008
  
• Analysis/PDE Summer Seminar (4 lectures), University of North Carolina, Department of Mathematics, July 2008
  
• Differential Equations Seminar, North Carolina State University, Department of Mathematics, April 2008
  
• Analysis and PDE Seminar, Johns Hopkins University, Department of Mathematics, March 2008
  
• Analysis/PDE Seminar, University of North Carolina, Department of Mathematics, December 2007
  
• PDE Seminar, University of California, Davis, Department of Mathematics, November 2007
  
• GMA Visions Seminar, University of North Carolina, Department of Mathematics, October 2007
  
• Nonlinear Waves and Dispersive Equations, Oberwolfach, Germany, September 2007
  
• Summer Microprogram on Nonlinear Partial Differential Equations, MSRI, August 2007
  
• VII Joint Meeting of AMS-SMM: Mathematical Physics Special Session, Zacatecas, Mexico, May 2007
  
• JAMI Conference: Nonlinear Dispersive Equations, Johns Hopkins University, Baltimore, MD, March 2007
  
• Analysis Seminar, McGill University (Montreal, Canada), Department of Mathematics, January 2007
  
• PDE/Analysis Seminar, University of California, Berkeley, Department of Mathematics, December 2006
  
• Mathematical Physics & Probability Seminar, University of California, Davis, Department of Mathematics, November 2006
  
• Applied Mathematics Seminar, Tohoku University (Sendai, Japan), Department of Mathematics, June 2006
  
• The 4th COE Symposium, Exploring New Science by Bridging the Particle-Matter Heirarchy, Sendai, Japan, June 2006
  
• Special Seminar, University of North Carolina at Chapel Hill, Department of Mathematics, February 2006
  
• Colloquium, Virginia Tech, Department of Mathematics, February 2006
  
• Candidate Talk, University of Rochester, Department of Mathematics, January 2006
  
• Geometric and Analytical Aspects of Nonlinear Dispersive Equations, MSRI, December 2005
  
• Postdoc Seminar, MSRI, September 2005
  
• FRG: Eigenfunctions of the Laplacian - Workshop I, University of Washington, Seattle, WA, July 2005
  
• Research Horizons Seminar, Georgia Institute of Technology, School of Mathematics, April 2005
  
• Analysis Seminar, Georgia Institute of Technology, School of Mathematics, November 2004
  
• Analysis Seminar, Princeton University, Department of Mathematics, November 2004
  
• NLW-HYKE: Summer School and Workshop on Nonlinear Wave Equations, Erwin Schroedinger Institute, Vienna, Austria, July 2004
• Analysis Seminar, UCLA, Department of Mathematics, October 2003
• CDSNS Seminar, Georgia Institute of Technology, School of Mathematics, October 2003
• Analysis Seminar, Johns Hopkins University, Department of Mathematics, March 2003
• Research Seminar, Xavier University, Department of Mathematics, February 2003
• Undergraduate Seminar, Xavier University, Department of Mathematics, February 2003
• Research Seminar, Grand Valley State University, Department of Mathematics, January 2003
• Analysis Seminar, Johns Hopkins University, Department of Mathematics, September 2002

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