I also spent the 2014-15 academic year at Crane Payment Innovations in Malvern PA, working on applied optics and machine learning problems.

- Bryan, K., and Leise, T., "Cloaking," in the
*Princeton Companion to Applied Mathematics*, September 2015. - Walter D., Bryan K., Stephens J., Bullmaster C., and Chakravarthy V.,
*Localization of RF Emitters using Compressed Sensing with Multiple Cooperative Sensors*, proceedings of NAECON 2012, Dayton OH, July 25-27 2012. - Bryan, K., Zhang, J., Pervez, N., Cox, M., Jia, X., and Kymissis, I.,
*Inexpensive photonic crystal spectrometer for colorimetric sensing*, Optics Express, Vol. 21, Issue 4, pp. 4411-4423 (2013), http://dx.doi.org/10.1364/OE.21.004411. -
*Making Do With Less: An Introduction To Compressed Sensing*with Tanya Leise at Amherst College, in SIAM Review's Education Section, Vol 55, No 3, 2013. -
*Transient Behavior of Solutions to a Class of Nonlinear Boundary Value Problems*, with Michael Vogelius , in the Quarterly of Applied Math 69(2), June 2011, p. 261-290. -
*Precise Bounds for Finite Time Blow-up of Solutions to Very General One Space-Dimensional Nonlinear Neumann Problems*, with Michael Vogelius , in the Quarterly of Applied Math 69(1), March 2011, p. 57-78. -
*A Tale of Two Masses*, PRIMUS 21(2), February 2011, p. 149-162.

I've begun some collaborations with Chris Earls at Cornell University and John Kymissis and his post-docs (and former post-docs) at Columbia University.

I've also written a nice series of papers suitable for undergraduates, with Tanya Leise at Amherst College. They have appeared in (or been submitted to) the Education Section of SIAM Review.

Other coauthors include REU students Melissa Vellela (now Melissa Nivala), Ron Ogborne, Nic Trainor, Rachel Krieger, Janine Haugh (now a full-fledged math professor at UNC Asheville), David McCune, and Professor Valdis Liepa (EE, University of Michigan),

Here is a complete list of papers, with abstracts.

Here's a preprint of an amusing result I "rediscovered" a few summers ago: Elementary Inversion of the Laplace Transform. It's very beautiful and simple, yet it seems to be practically unknown---no standard book on the Laplace Transform has it and no one I asked about it had ever heard of the result. Ironically and tragically, I finally discovered that the result was proved by Emil Post in 1930. I found this out quite by accident while randomly browsing through a Dover book in a Border's bookstore! I'm going to submit this to the Monthly relatively soon.

- A set of notes for a short course in inverse problems that I taught at the Air Force Academy in 2011. It's a gentle overview for undergraduates and nonspecialists, and the slides I used are here too.
- Some notes and Maple notebooks I wrote on RSA encryption for a series of talks I gave in our Math Seminar (which I often organize) in the spring of 1998.
- Many other notes on mathematical topics I write for myself or students. No claim of accuracy or completeness is made!

- Here's a web site with many cool links to math resources.