- The influence of complex geometries (particularly in the
nanoscale) on solutions of partial differential equations,
especially for wave phenomena and electromagnetism — analytical theory, numerics, and design of devices and phenomena. (See, for example, photonic crystals.)
- High-performance computation, such
as fast Fourier transforms, solvers
electromagnetism, and large-scale optimization.
Read about the other members of our research group.
We also have close collaborations with various experimental and theoretical groups at MIT and elsewhere; see also the Ab Initio Physics Group at MIT.
See the list of our publications (along with
abstracts and, in most
cases, the papers in PDF format) to find out what we have been up to.
We may also have a few preprints available
online. (See also other publications from
the ab-initio group.) We also have a new textbook on the
basic ideas behind some of our research:
I received my Ph.D. in physics from MIT in 2001, as well as BS
degrees in physics, mathematics, and computer science from MIT in 1995,
with post-doctoral positions at MIT and Harvard. My Ph.D. thesis was
published as a book by
Kluwer in 2002 (sans color, unfortunately); you
can read the introduction
online. I grew up in St.
Charles, Illinois and attended high school at the Illinois
Mathematics and Science Academy (IMSA).
My curriculum vitae is also online, but may not be up to date.
- 18.03 Differential Equations
(Fall 2005 recitations)
- 18.06: Introduction to Linear Algebra (Fall 2007, Spring 2009), Spring/Fall 2017, Fall 2018, spring 2022, and fall 2022.
- 18.065: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning in spring 2023.
- 18.303: Linear Partial Differential Equations — Analysis and Numerics (Falls 2010-2016)
- 18.335: Introduction to Numerical Methods
(Fall 2008-2013, Spring 2015, 2018-2021)
- 18.336: Numerical Methods for Partial Differential Equations
- 18.369: Mathematical Methods in Nanophotonics
(Spring 2008, 2009, 2010, 2012, 2014, 2016, 2018, 2020, and Fall 2021)
- 18.S096: Matrix Calculus (IAP 2022, 2023).
Crystals: Periodic Surprises in Electromagnetism: 2003-2018 IAP seminar and related materials
- Some Brief Mathematical Notes on various topics, mostly as a supplement to the above courses.
photos here, newer ones here, and the latest ones here. I've recently taken up guitar with Sam Davis and recorder with John Tyson. My daughter and I make silly songs together.