Research
 support:
 National
Science Foundation


Wetterhahn Award
and
Jeffe Fellowship

Bio and CV;
Research and teaching statements (2012);
tenure packet (2010)

Numerical analysis and scientific computing,
computational partial differential equations: Helmholtz equation, high frequency waves, eigenvalue, scattering and periodic problems, photonic crystals, heat equation, corner singularities, boundary integral equations.
 Mathematical physics: quantum chaos and ergodicity, Laplacian eigenfunctions, scarring,
billiards, random plane waves.
(Also see old physics graduate work).
 Applied mathematics: mathematical ecology (animal home range modeling),
medical inverse problems (neuroscience, optical tomography), mathematics of music.
Publications and talks
Our group:


Adrianna Gillman, an expert on fast direct
solvers for integral equations, joined us as a JWY Instructor
in July 2011, and will start tenuretrack at Rice July 2014.
 

Min Hyung Cho,
an expert on fast multipole and layered media, joined us as an IACM
Instructor in July 2012.
 
 Lin Zhao started as a graduate student on
boundary integral methods for Laplace eigenvalue problems in June 2012,
partially supported by NSF.
 
 Larry (Yuxiang) Liu
(Physics dept) started as a graduate student in scattering from periodized bodies of revolution in Dec 2012,
partially supported by NSF and the Neukom Institute.
 
 John Conley '15,
Presidential Scholar, modeling waveguides and solar cells, 20132014.

Prospective grad students: although the 1styr qual is puremath oriented,
the 2ndyr need not be, and
we have an expanding applied/computational group at Dartmouth. Do apply!
Seminars and conferences: I started and corun the
Applied and Computational Mathematics Seminar.
I am an organizer of the NSFCBMS Conference
of Fast Direct Solvers for Elliptic PDE, June 2220, 2014.
Collaboration & mentoring:
 Main collaborators:
Leslie Greengard,
Andrew Hassell,
Adrianna Gillman,
Gunnar Martinsson,
Timo Betcke,
...
 Prior students:
 James Brofos '15,
adaptive schemes for close evaluation of layer potentials, NSFfunded undergraduate research, summer 2013.
 Ben Southworth '13
(coadvised with Brenden Epps), summer 2013.
 Brad Nelson '13
(Senior thesis; CookRichter award; Neukom prize;
integral equations in gradedindex media, 20122013)
 Vipul Kakkad '13 (Presidential Scholar, optimizing bell mode frequencies, 2012)
 Kyle Konrad '12 (Senior thesis, high honors, quantum chaos nodal domains, 20112012. Picture used in this
CRM poster!. Work supported by a Neukom Scholarship).
 Hahn Nguyen '14 (WISP intern,
close evaluation of layer potentials, poster, 2011)
 Taylor Sipple '13 (Presidential Scholar, polygonal eigenmodes, 2011)
 Kathleen Champion '11 (Presidential Scholar & senior thesis, cell tracking with MCMC and 3D data w/ Gladfelter Lab, 20102011)
 Zoe Lawrence, '10 (spatial dynamics of disease, coadvisor Dorothy Wallace, 2010)
 Yong Su '09 (Senior thesis, spectral methods for capacitance with corners, 20089)
 Evan Tice '09 (Senior thesis, cell division video tracking w/
Gladfelter Lab, 20089; awarded Kemeny Prize
for his code)
 Emmanuel Mensah '09 (Indep. study, inverse source problem, published in DUJS)
 Matt Mahoney, Ph.D. '09 (graded index materials, 20067)
 Chetan Mehta '08 (Senior thesis, optical tomography, 20078)
 Chor Lam '08 (Presidential Scholar, billiards, 20078)
 Vissuta Jiwariyavej '09 (WISP intern, acoustics & prime numbers, 20067)
Teaching
students should check out our
applied courses roadmap
 Math 116: Great papers in numerical analysis
and computational algorithms.
(Spring 2014). Graduatelevel; description.
 Math147: Graduate Teaching Seminar
(Summer 2012, 2013, 2014). Nationallyrecognized instructor training.
 Math 56: Computational and Experimental Mathematics (Spring 2013, 2014).
New course on computation tools in pure and applied math:
fast Fourier transform, millions of digits...
 Math126/116: Numerical analysis for PDEs and
wave scattering
(Winter 2006, Fall 2008, Winter 2012).
Gradlevel: numerical, quadrature, integral equations,
layer potentials, fast methods, coding... description
 Math5: The Mathematics of Music and Sound
(Spring 2007, Fall 2008, 2010, and 2011). How instruments work, voice, ear, Fourier, signal analysis, acoustics, waves...

Math53: Chaos! (Fall 2007, 2009, 2011).
Chaotic dynamics, maps, flows, fractals, applications...
flyer.

Math46: Introduction to Applied
Mathematics (Springs 2007, 2008, 2009, 2011). Core analytical tools formodeling, ODE/PDEs, integral equations, Greens functions, applications...
 Math11: Multivariable Calculus
(Fall 2010).

Math23: Differential Equations (Fall 2005, Fall 2007).
My Matlab demo
of Taylor series in complex plane
(needs show_zser)

Math22: Linear Algebra with Applications (Summer 2006).

Math50: Statistical Inference (Winter 2006).
Probability, Bayes...

Business Calculus (Fall 2004, NYU). Contour worksheet.

Mathematical Wave Dynamics (Spring 2004, NYU).
New. Honors course on theory and numerics of waves, with
Oliver Buhler.

Linear Algebra (Fall 2003, NYU). Inclass
worksheets
(DjVu format
[plugin]), and
math exam notes.

Multivariable Calculus (Spring 2003, NYU).

Undergraduate Math Lab (Fall 2002, NYU).
New; honors class on prime numbers, random matrices, graphs, with
Peter Sarnak,
Steve Miller.

Laboratory Electronics (Fall 2001, Harvard). Paul Horowitz and Tom Hayes,
gods of circuit design.
Service to College
Old Personal Page
media projects, music, photos, wind energy, electronics...

Periods, pitches & pipes:
a new middleschool teaching module connecting music and math.
Megan Martinez, Alex Barnett (via GK12 and NSF, 2013)
Images from our group used for CRM 2012 poster:
RESOURCES...
Quasiperiodic scattering
from dielectric gratings:
My front cover, Notices of the AMS, Jan 2008:
MFS basis stability for the Helmholtz equation:
Math is a
myth in Wales
Dartmouth crime map
Check email
