Research
 support:
 National
Science Foundation


Wetterhahn Award
and
Jeffe Fellowship

Bio and CV;
Professional statement (2016)

Computational partial differential equations: wave scattering (the Helmholtz equation), periodic diffraction problems, variable media, highfrequency eigenvalue problems, acoustics, optics, fluid flow (Stokes).
 Numerical analysis: fast algorithms, integral equations, quadrature, spectral methods.
 Computational biological inverse problems:
spike sorting (neuroscience), cryo electron microscopy.
 Mathematical physics: quantum chaos, random plane waves. (Also see old research and graduate work.) Mathematics of music.
Note: As of late 2014,
I am also a consulting senior research scientist at the CCB at the new
Flatiron Institute in NYC, working on algorithms and software for neural spike sorting, cryoEM, and other numerical problems. I will spend a significant fraction of each year there over the period 20152018.
Publications, talks, and notes
Our group:

 Larry (Yuxiang) Liu
(Physics) started as a graduate student in scattering from periodized bodies of revolution in Jan 2013,
partially supported by NSF and the Neukom Institute Congratulations Larry on receiving the Ph.D. in June 2016!
Larry is moving in Oct 2016 to a postdoc in applied physics at Yale.
 

Paula Chen '17. Senior thesis on improving spike sorting algorithms.
 

Matthew Jin '17. NSFfunded undergraduate researcher
measuring topology statistics of nodal sets of
random plane waves.

Prospective grad students: although the 1styr qual is puremath oriented,
the 2ndyr need not be, and
we have an expanding applied/computational group at Dartmouth. Do apply!
Seminars and conferences: I started and corun the
Applied and Computational Mathematics Seminar.
I am an organizer for the workshop
Modern Advances in Computational and Applied Mathematics at Yale, June 2017.
Collaboration & mentoring:
 Main collaborators:
Leslie Greengard,
Andrew Hassell,
Shravan Veerapaneni,
Jeremy Magland,
Adrianna Gillman,
Gunnar Martinsson
...
 Prior group members and advisees:
 Min Hyung Cho.
Computational optics, electromagnetics, fast algorithms, layered media.
IACM Instructor July 2012  June 2015.
Tenuretrack at UMASS Lowell started July 2015.
 Lin Zhao, Ph.D June 2015. Thesis topic:
integral equations for Laplace eigenvalue and doublyperiodic electrostatics and Stokes flow problems. Now a research associate at INTECH.

Adrianna Gillman. Research
areas: fast direct solvers, PDEs, integral equations. JWY Instructor
July 2011  June 2014. Tenuretrack at Rice started July 2014.

John Conley '15,
Presidential Scholar, optimizing multilayer solar cells, 20132014. codes.
 James Brofos '15,
adaptive schemes for close evaluation of layer potentials, NSFfunded undergraduate research, summer 2013.
 Ben Southworth '13
(coadvised with Brenden Epps), summer 2013. (went to Boulder applied math PhD program)
 Brad Nelson '13.
(Senior thesis; CookRichter award; Neukom prize;
integral equations in gradedindex media, 20122013)
(went to Stanford applied math PhD program)
 Vipul Kakkad '13 (Presidential Scholar, optimizing bell mode frequencies, 2012). codes
 Kyle Konrad '12 (Senior thesis, high honors, quantum chaos nodal domains, 20112012. Picture used in this
CRM poster!. Support from Neukom Scholarship). codes.
 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, 20102011) (went to U Wash applied math PhD program)
 Zoe Lawrence, '10 (spatial dynamics of disease, coadvisor Dorothy Wallace, 2010)
 Yong Su '09 (Senior thesis, Tools for the capacitance of the cube and Laplace eigenfunctions on the sphere, 20089)(went to Stanford statistics PhD program)
 Evan Tice '09 (Senior thesis, cell division video tracking w/
Gladfelter Lab, 20089; 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, 20067)
 Chetan Mehta '08 (Senior thesis, optical tomography, 20078)
 Chor Lam '08 (Presidential Scholar, billiards, 20078) (went to Cornell math PhD program)
 Vissuta Jiwariyavej '09 (WISP intern,
acoustics & prime numbers, 20067)
Teaching
students should check out our
applied courses roadmap

Math22: Linear Algebra with Applications (Summer 2006, Fall 2016).

Math53: Chaos! (Fall 2007, 2009, 2011, 2015).
Chaotic dynamics, maps, flows, fractals, applications...
flyer.
 Math11: Multivariable Calculus
(Fall 2010, 2015).
 Math 116: Great papers in numerical analysis
and computational algorithms.
(Spring 2014). Graduatelevel; description.
 Math147: Graduate Teaching Seminar
(Summer 2012, 2013, 2014). Nationallyrecognized instructor training.
 Math 56: Computational and Experimental Mathematics (Spring 2013, 2014).
New course on computation tools in pure and applied math:
fast Fourier transform, millions of digits...
 Math126/116: Numerical analysis for PDEs and
wave scattering
(Winter 2006, Fall 2008, Winter 2012).
Gradlevel: 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...

Math46: Introduction to Applied
Mathematics (Springs 2007, 2008, 2009, 2011). Core analytical tools formodeling, ODE/PDEs, integral equations, Greens functions, applications...

Math23: Differential Equations (Fall 2005, Fall 2007).
My Matlab demo
of Taylor series in complex plane
(needs show_zser)

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). Inclass
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.
Service to College on Student Life
 Letter to President Hanlon on Sexual Assault and the Greek System (Sept 2013). Contains useful references for anyone who cares about reducing rape on campus.
 Opening statement for The Great Debate on the future of the Greek system at Dartmouth (April 2014). Accompanying reading list documenting effects of Greek life on student wellbeing.
 Letter to The Dartmouth re article in Green Key special issue (May 2014).

Statement for Moving Dartmouth Forward Committee on Extreme Behaviors (Aug 2014).
 Our
letter signed by at least 239 faculty, on phasing out the Greek system.
(Nov 2014). Faculty voted on this issue 11/3/14: 116 for, 13 against, 3 abstain.
Old Personal Page
media projects, music, photos, wind energy, electronics...

Images from our group used for SMS/CRM 2015 poster:
Periods, pitches & pipes:
a new middleschool teaching module connecting music and math.
Megan Martinez, Alex Barnett (via GK12 and NSF, 2013)
RESOURCES...
Quasiperiodic scattering
from dielectric gratings (2010):
My front cover, Notices of the AMS (2008):
MFS basis stability for the Helmholtz equation
(2004):
Math is a
myth in Wales
Dartmouth crime map
Check email
