Present. Since January 2009 I've been an assistant professor at UNM.
Past. From August 2006 until December 2008, I was in the
Division of Applied Mathematics at Brown University, working for
Hesthaven and physics groups at Cornell and Caltech as part of
an NSF grant devoted to spectral methods for the Einstein equations.
Over a number of years members of the Caltech-Cornell-CITA collaboration
(chiefly Lawrence E. Kidder, Harald P. Pfeiffer, and Mark A. Scheel)
have written a multidomain spectral code, SpEC
(spectral Einstein code).
The relativity groups at Caltech, Cornell, and CITA (Canadian Institute
of Theoretical Astrophysics) are using SpEC to generate and evolve initial
data describing the inspiral of binary blackholes. I've incorporated
various implicit-explicit (IMEX) ODE solvers into the TimeStepper
module of SpEC, and the project [with H. Pfeiffer (CITA) and
Geoffrey Lovelace (CSU, Fullerton)] aims to sidestep the Courant limit
in binary evolutions by using an IMEX time-stepper such as additive
Runge-Kutta. This should be feasible since the solutions (well
before merger) are quasi-stationary in a co-rotating frame.
Over the 2005-2006 academic year I worked as a postdoc in
Mathematics & Statistics here at UNM
for Thomas M. Hagstrom
(now at SMU) on radiation boundary conditions and numerical wave
propagation, and I'm still working on boundary conditions for the wave
equation in the presence of sharp corners or edges. Over 2004-2005 I was
a research assistant professor of physics at
the CGWA in Brownsville
TX, working for
Richard H. Price
on the periodic standing wave (PSW)
approximation for binary inspiral. This ongoing work involves
application of spectral methods with integration preconditioning to
the mixed-type PDE cropping up in PSW problems.
Education. I did graduate work in applied mathematics at the
University of North
Carolina, studying numerical solutions to partial differential equations
under Michael L.
Minion. My dissertation, Rapid
Evaluation of Radiation Boundary Kernels for Time-Domain Wave
Propagation on Blackholes, numerically implemented
radiation outer boundary conditions for the Regge-Wheeler equation, an
incarnation of the (singly) confluent Heun equation. This work was based
on an approach developed for the ordinary wave equation by Alpert,
Greengard, and Hagstrom [SIAM J. Numer. Anal. 37 (2000) 1138].
Far past. Earlier I wrote a physics dissertation in general relativity
(UNC, June 1994) under the direction of James W. York. My physics dissertation
reformulated the Brown-York two-surface integral definitions of gravitational
stress, energy, and momentum in terms of Ashtekar variables. The Brown-York
expressions stem from Hamilton-Jacobi theory as applied to the "Trace K" action,
the Einstein-Hilbert action plus appropriate boundary terms. Ashtekar variables
are a Yang-Mills chart (the Hamiltonian variables are A and E) on
the phase space of general relativity. As a relativist, I worked as a postdoc
at the Inter-University Centre for Astronomy and Astrophysics (Pune, India)
from 1994 to 1995 and at the Technische Universitaet Wien (Vienna, Austria)
from 1995 to 1997. My interests in theoretical GR center around definitions of
gravitational energy, and I have collaborated with Alexander N. Petrov of Moscow State
University's Sternberg Astronomical Institute.
Teaching. Over the years, I've gotten
interested in teaching undergraduate math and physics, and have
experimented with several different instruction methods
(see my Teaching Statement). This Fall 2013 I am teaching
CS-Math 471 (introduction to scientific computing)
and Math 576 (numerical linear algebra).
The 471 course webpage is on UNM Learn.