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),
inverse problems in medical imaging (diffuse optical tomography), mathematics of music.
Publications and talks
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!
Adrianna Gillman, an expert on fast direct
solvers for integral equations, joined us as a JWY Instructor
in July 2011.
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, 2013-2014.
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:
students should check out our
applied courses roadmap
- Main collaborators:
- Prior students:
- James Brofos '15,
adaptive schemes for close evaluation of layer potentials, NSF-funded undergraduate research, summer 2013.
- Ben Southworth '13
(co-advised with Brenden Epps), summer 2013.
- Brad Nelson '13
(Senior thesis; Cook-Richter award; Neukom prize;
integral equations in graded-index media, 2012-2013)
- 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)
media projects, music, photos, wind energy, electronics...
- Math147: Graduate Teaching Seminar
(Summer 2012, 2013). Nationally-recognized instructor training.
- Math 56: Computational and Experimental Mathematics (Spring 2013).
New course on computation tools in pure and applied math:
fast Fourier transform, millions of digits...
- Math126/116: Numerical analysis for PDEs and
(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...
Math53: Chaos! (Fall 2007, 2009, 2011).
Chaotic dynamics, maps, flows, fractals, applications...
Math46: Introduction to Applied
Mathematics (Springs 2007, 2008, 2009, 2011). Core analytical tools formodeling, ODE/PDEs, integral equations, Greens functions, applications...
- Math11: Multivariable Calculus
Math23: Differential Equations (Fall 2005, Fall 2007).
My Matlab demo
of Taylor series in complex plane
Math22: Linear Algebra with Applications (Summer 2006).
Math50: Statistical Inference (Winter 2006).
Business Calculus (Fall 2004, NYU). Contour worksheet.
Mathematical Wave Dynamics (Spring 2004, NYU).
New. Honors course on theory and numerics of waves, with
Linear Algebra (Fall 2003, NYU). In-class
math exam notes.
Multivariable Calculus (Spring 2003, NYU).
Undergraduate Math Lab (Fall 2002, NYU).
New; honors class on prime numbers, random matrices, graphs, with
Laboratory Electronics (Fall 2001, Harvard). Paul Horowitz and Tom Hayes,
gods of circuit design.
Periods, pitches & pipes:
a new middle-school teaching module connecting music and math.
Megan Martinez, Alex Barnett (via GK12 and NSF, 2013)
Images from our group used for CRM 2012 poster:
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