Alex Barnett

Associate Professor, Applied Mathematics

How to reach me:
Kemeny, room 206, tel (603) 646-3178
email:

Applied Math Lab: Kemeny, room 209

By physical mail:
Department of Mathematics
6188 Kemeny Hall
Dartmouth College
Hanover, NH, 03755

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:
- Brad Nelson '13 (Undergraduate Research Grant, graded-index media, 2012)
- Vipul Kakkad '13 (Presidential Scholar, optimizing bell mode frequencies, 2012)
- Kyle Konrad '12 (Senior thesis, quantum chaos nodal domains, 2011-2012. Picture used in this CRM poster!. Work supported by a Neukom Scholarship).
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...
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). In-class 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.