Research
| support:
| National
Science Foundation
|
|
Wetterhahn Award
and
Jeffe Fellowship
|
Bio and CV;
Professional statement and tenure file (21MB);
older overviews: informal / more technical
-
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),
inverse problems in medical imaging (diffuse optical tomography), mathematics of music.
Publications and talks
Job postings:
We are delighted that Adrianna Gillman, an expert on fast direct PDE solvers, joined us as a JWY Instructor starting July 2011.
I am also looking for graduate students: although the quals are relatively pure-math focused,
we do have an expanding applied group at Dartmouth!
Seminars and conferences: I started and run the
Applied and Computational Mathematics Seminar.
I was an organizer of the
International Conference on Spectral Geometry, July, 2010.
Laurent Demanet and I have organized ICIAM 2011 minisymposia on periodic and high frequency numerical waves.
Collaboration & mentoring:
- Main collaborators:
Leslie Greengard,
Andrew Hassell,
Timo Betcke,
Adrianna Gillman,
...
- Current students:
- Prior students:
- 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, 2010-2011)
- Zoe Lawrence, '10 (spatial dynamics of disease, co-advisor Dorothy Wallace, 2010)
- Yong Su '09 (Senior thesis, spectral methods for capacitance with corners, 2008-9)
- Evan Tice '09 (Senior thesis, cell division video tracking w/
Gladfelter Lab, 2008-9; 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, 2006-7)
- Chetan Mehta '08 (Senior thesis, optical tomography, 2007-8)
- Chor Lam '08 (Presidential Scholar, billiards, 2007-8)
- Vissuta Jiwariyavej '09 (WISP intern, acoustics & prime numbers, 2006-7)
Teaching
students should check out our
applied courses roadmap
-
Math126/116: Numerical analysis for PDEs and
wave scattering
(Winter 2006, Fall 2008, Winter 2012).
Grad-level: 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...
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Math53: Chaos! (Fall 2007, 2009, 2011).
Chaotic dynamics, maps, flows, fractals, applications...
flyer.
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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).
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Math23: Differential Equations (Fall 2005, Fall 2007).
My Matlab demo
of Taylor series in complex plane
(needs show_zser)
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Math22: Linear Algebra with Applications (Summer 2006).
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Math50: Statistical Inference (Winter 2006).
Probability, Bayes...
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Business Calculus (Fall 2004, NYU). Contour worksheet.
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Mathematical Wave Dynamics (Spring 2004, NYU).
New. Honors course on theory and numerics of waves, with
Oliver Buhler.
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Linear Algebra (Fall 2003, NYU). In-class
worksheets
(DjVu format
[plugin]), and
math exam notes.
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Multivariable Calculus (Spring 2003, NYU).
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Undergraduate Math Lab (Fall 2002, NYU).
New; honors class on prime numbers, random matrices, graphs, with
Peter Sarnak,
Steve Miller.
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Laboratory Electronics (Fall 2001, Harvard). Paul Horowitz and Tom Hayes,
gods of circuit design.
Personal
media projects, music, photos, wind energy, electronics...
|
Images from our group used for CRM 2012 poster:
RESOURCES...
Quasi-periodic 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
Check email
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