David Borthwick

Professor of Mathematics
Emory University

David Borthwick

Contact Information

Address: Dept. of Math/CS
Emory University
Atlanta, GA 30322 USA
Office: W417 Math & Science Center
Email: davidb@mathcs.emory.edu
Phone: (404) 727-4993


My interests are global and geometric analysis, differential geometry, and mathematical physics.

I wrote the book: Spectral Theory of Infinite-Area Hyperbolic Surfaces, Birkhauser, 2007.  For more information (including errata) see the book's

book cover

Slides from some talks:

  1. Riemann’s zeros and the rhythm of the primes, given at Emory Nov. 2009 to celebrate the 150th anniversary of the Riemann hypothesis.

  2. Spectral theory on hyperbolic surfaces, from 3 expository lectures given at the Dartmouth Spectral Geometry meeting, July 2010.

  3. Sharp geometric bounds on resonances for surfaces with hyperbolic ends, research talk given at the Penn State Spectral and Scattering Theory conference, August 2010.

Some recent research articles:

  1. D. Borthwick, Sharp geometric upper bounds on resonances for surfaces with hyperbolic ends, Analysis & PDE 5 (2012), 513--552. (arXiv preprint)

  2. D. Borthwick, Introduction to spectral theory on hyperbolic surfaces, Proc. Symp. Pure Math. 84 (2012), 3--48. (preprint)

  3. D. Borthwick and C. Crompton, Resonance asymptotics for Schr\"odinger operators on hyperbolic space. (arXiv preprint)

  4. D. Borthwick and C. Guillarmou, Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds. (arXiv preprint)

  5. D. Borthwick, Distribution of resonances for hyperbolic surfaces, to appear in Experimental Math. (arXiv preprint)

  6. D. Borthwick and P.~Philipp, Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends. (arXiv preprint)

Publications available at OpenEmory.

Academic History


1988 A.B., Princeton University
1993 Ph.D. in Physics, Harvard University (advisor: Arthur Jaffe)


1993-96 Assistant Professor, University of Michigan
1996-97 NSF Posdoctoral Research Fellow, University of California at Berkeley
1997-2002 Assistant Professor, Emory University
2002-2009 Associate Professor, Emory University
2009- Professor, Emory University

Grants and awards

1994 Rackham Faculty Fellowship, University of Michigan
1994-97 NSF Research Grant in Modern Analysis
1996-99 NSF Postdoctoral Research Fellowship
2002-05 NSF Research Grant in Geometric Analysis
2009-12 NSF Research Grant in Analysis

Curriculum Vitae

Last modified Oct., 2013.