Research
| support: National
Science Foundation
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Informal introduction,
more technical, or
research statement; CV
- Numerical methods for the Dirichlet eigenproblem (`drum problem'),
high-frequency waves, elliptic boundary-value problems.
Global approximation and boundary methods.
- Semiclassical study (mainly numerical)
of eigenfunctions of PDEs in chaotic
systems, an area of mathematical physics known as quantum chaos.
Quantum ergodicity, scars, billiards, dynamical tunneling. (Also see physics graduate work).
- Mathematical ecology and diffusion modeling of animal home ranges.
- Inverse problems in medical imaging:
Diffuse Optical Tomography for functional brain imaging,
numerical methods for diffusion in complex geometries,
Bayesian statistical inversion.
Seminars: I started and co-run the new
Applied and Computational Mathematics Seminar with
Petia Vlahovska
Publications and talks
Collaboration & mentoring:
- (Some) collaborators: Timo Betcke,
Leslie Greengard,
Paul Moorcroft, Andrew Hassell,
Amy Gladfelter
...
- Graduate students:
Matt Mahoney
(2006-7)
- Undergraduate students:
- Chetan Mehta (
Senior thesis, optical tomography, 2007-8)
- Chor Lam (Presidential scholar, 2007-8)
- Evan Tice (cell division video tracking, w/ Gladfelter Lab, 2008;
for which received Kemeny Prize)
- Vissuta Jiwariyavej (WISP intern, acoustics & prime numbers, 2006-7)
Teaching
teaching statement...
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Math5: The Mathematics of Music and Sound
(Spring 2007, Fall 2008). New; how instruments work, voice, ear, Fourier, signal analysis, acoustics, waves...
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Math116: Numerical methods for PDEs and
waves
(Winter 2006, Fall 2008). Grad-level: integral equations, scattering,
layer potentials...
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Math46: Introduction to Applied Mathematics (Springs 2007, 2008, 2009). New; core analytical tools for ODE/PDEs, integral equations, Greens functions, applications...
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Math53: Chaos! (Fall 2007, 2009).
New; chaotic dynamics, maps, flows, fractals, applications...
flyer.
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Math23: Differential Equations (Fall 2007, Fall 2005).
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 research 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
includes media projects, wind energy, music, electronics...
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My front cover, Notices of the AMS, Jan 2008:
RESOURCES...
Photonic band structure,
fast sweep of Brillouin zone:
MFS basis stability for the Helmholtz equation:
Dirichlet eigenfunctions of the mushroom billiard:
Random plave waves
Math is a
myth in Wales
Check email
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