Research
| support:
| National
Science
Foundation
|
|
Wetterhahn Award
and
Jeffe Fellowship
|
Bio and CV;
Research and teaching statements (2012);
tenure packet (2010)
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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
| Our group:
|
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Adrianna Gillman, an expert on fast direct
solvers for integral equations, joined us as a JWY Instructor
in July 2011.
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Min Hyung Cho,
an expert on fast multipole and layered media, joined us as an IACM
Instructor in July 2012.
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| Lin Zhao started as a graduate student on
boundary integral methods for Laplace eigenvalue problems in June 2012,
partially supported by NSF.
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| 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.
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| Brad Nelson '13,
senior thesis (supported by Cook-Richter award spring 2012,
won 1st prize in our poster session),
integral equations for graded-index media.
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Prospective grad students: although the 1st-yr qual is pure-math oriented,
the 2nd-yr need not be, and
we have an expanding applied/computational group at Dartmouth. Do apply!
Seminars and conferences: I started and co-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 organizeda SIAM CSE 2013 minisymposium
on volume methods for the high-frequency Helmholtz equation.
Collaboration & mentoring:
- Main collaborators:
Leslie Greengard,
Andrew Hassell,
Adrianna Gillman,
Gunnar Martinsson,
Timo Betcke,
...
- Prior students:
- Vipul Kakkad '13 (Presidential Scholar, optimizing bell mode frequencies, 2012)
- Kyle Konrad '12 (Senior thesis, high honors, quantum chaos nodal domains, 2011-2012. 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, 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
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Math 56: Computational and Experimental Mathematics (Spring 2013).
New course on computation tools in pure and applied math:
fast Fourier transform, millions of digits...
- Math147: Graduate Teaching Seminar
(Summer 2012, 2013). Nationally-recognized instructor training.
- 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...
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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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