David Borthwick

Professor of Mathematics
Director of Graduate Studies

Emory University

David Borthwick


Contact Information

Address: Dept. of Math/CS
Emory University
Atlanta, GA 30322 USA
Office: W417 Math & Science Center
Email: dborthw@emory.edu

Research

My interests are spectral theory, global and geometric analysis, and mathematical physics. Preprints of my published articles are posted on the arXiv and also at OpenEmory.

Much of my recent research has to do with the distribution resonances of hyperbolic surfaces of infinite area. Here is a sample plot showing roughly 18,000 resonances of a hyperbolic funneled torus:

resonance plot


Books

SP

Spectral Theory is a text covering basic functional analysis with an emphasis on spectral theory. The first half of the book introduces the theory of Hilbert spaces and operators, leading up to a proof of the spectral theorem. In the second half, this theory is applied to develop the spectral theory for some important examples, such as the Dirichlet Laplacian and Schrodinger operators. The text is published by Springer in the GTM series. Available directly from the publisher or from Amazon.

A current list of errata is available here. Please email me if you find an issue that is not on the list.

PDE

Introduction to Partial Differential Equations is a text for advanced undergraduate or beginning graduate course on PDE. My primary goal in this book was to make the theory accessible without requiring extensive analysis prerequisites. The text is published by Springer in the Universitext series. Available directly from the publisher or from Amazon.

A current list of errata is available here. Please email me if you find an issue that is not on the list. The first printing had additional mistakes which were corrected as of Spring 2018, in both print and online editions.

STHS

Spectral Theory of Infinite-Area Hyperbolic Surfaces has a second edition as of 2016, Volume 318 in the Progress in Mathematics series published by Birkhauser. Available directly from the publisher or from Amazon.

A current list of errata is available here.


Videos

Overtones

Overtones and Musical Intervals, a video lecture on the mathematical origins of musical intervals and scales. This is an expanded and edited version of a presentation I did for the online Mathapalooza event at the 2021 Atlanta Science Festival.

Glass

A video featuring the 3rd movement from Phillip Glass: Symphony No. 3. The parts were all recorded remotely during the 2020 pandemic lockdown, and I did the arranging, mixing, and video production. I also cover 7 different viola parts, and joined by various family members and friends.


Academic History

Education

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

Career

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

Curriculum Vitae


Other Activities




Last modified December, 2022.