Steven G. Johnson Professor of Applied Mathematics and Physics Massachusetts Institute of Technology stevenj ατ math døt mit døt edu, MIT Room 2-345 (map), 617-253-4073 orcid.org/0000-0001-7327-4967, google scholar Nanostructures and Computation Group • Papers/Preprints • Collaborators

Research Interests

• 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 for numerical 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.

Publications

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:

• John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robert D. Meade, Photonic Crystals: Molding the Flow of Light, second edition (Princeton Univ. Press, 2008). See our page on the second edition for more information, including links to read the book online and/or purchase a printed copy.

Background

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.

Teaching

• 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 (Spring 2006)
• 18.369: Mathematical Methods in Nanophotonics (Spring 2008, 2009, 2010, 2012, 2014, 2016, 2018, 2020, Fall 2021, and Spring 2024)
• 18.S096: Matrix Calculus (IAP 2022, 2023, 2024).
• Photonic 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.

Personal

Embarrassing old 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.