Current/future teaching:

• EIDMA/DIAMANT minicourse, March 2008

Past teaching:

• Paradoxes and the Foundations of Mathematics, SIMUW 2007
• The Mathematics of Error Correcting Codes, taught with Nati Linial, Madhu Sudan, and Alex Samorodnitsky, Oberwolfach seminar (for graduate students and postdocs), October 2006
• Theory of Equations, SIMUW 2006 (see here for problem sets and handouts)
• Math 581G (Exceptional Structures in Mathematics), taught with Charles Doran, University of Washington, Fall 2005
• Sphere Packings: Exceptional Geometric Structures and Connections to other Fields, taught with Robert Griess and Achill Schuermann, Oberwolfach seminar (for graduate students and postdocs), November 2005
• Combinatorics, SIMUW 2005
• Theory of Equations, SIMUW 2004
• Combinatorics, SIMUW 2003
• Math 583CA (Mathematical Logic), University of Washington, Spring 2003
• Math 1b (Calculus), Harvard University, Spring 2000
• Tutorial on mathematical logic and foundations of mathematics, Harvard University, Fall 1999
• Tutorial on cryptography, Harvard University, Spring 1999
• Math 21a (Multivariable Calculus), Harvard University, Fall 1998
• Tutorial on probabilistic proof systems, Harvard University, Fall 1997
• Designed and taught a ten-session math class for fourth graders in the spring of 1997 for the Math Circle program
• Course assistant for Math 212a (graduate Real Analysis), Harvard University, Fall 1996
• Counselor at the Program in Mathematics for Young Scientists at Boston University during the summers of 1992 through 1995, head counselor in 1996, and recitation instructor in 1997 and 1998
• Designed and taught an "Introduction to Proofs" class (not for credit) at MIT with Ben Raphael during January of 1994 and 1995, to prepare non-majors for taking proof-based mathematics classes
• Designed and taught ten-week weekend courses in mathematics for high school students as part of MIT's Educational Studies Program in the springs of 1992 through 1995, as well as one-weekend fall courses

A few definitions: At Harvard a tutorial is a two hour per week course for advanced undergraduates designed and taught by a graduate student (who both lectures and also supervises individual projects on which the students write term papers and deliver lectures). A course assistant runs weekly review classes to supplement the main lectures and grades problem sets.

Graduate students:

• Stephanie Vance, University of Washington, current Ph.D. student
  • Stephanie is working on sphere packing.
• Chris Hanusa, University of Washington, Ph.D. received 6/2005
  • Dissertation: A Gessel-Viennot-type Method for Cycle Systems and Applications to Aztec Pillows

Summer research students supervised:

• Yakov Kerzhner, Microsoft Research, 6/2007 through 8/2007
  • Yakov worked on hyperbolic sphere packing.
• Blair Sullivan, Microsoft Research, 6/2007 through 8/2007
  • Blair worked on graph theory.
• Jeffrey Wang, Microsoft Research, 6/2007 through 8/2007
  • Jeffrey worked on packing and energy minimization.
• Bryden Cais, Microsoft Research, 6/2005 through 8/2005
  • Bryden worked on irrationality proofs and energy minimization.
• Brandon Ballinger, Noah Giansiracusa, and Elizabeth Kelly, University of Washington VIGRE program, 9/2004 through 6/2005
• We worked on a numerical study of energy-minimizing configurations in high dimensions.
• Jonathan Kelner, Microsoft Research, 6/2004 through 8/2004
  • Jon worked on several long-term projects of his, in particular finding Nash equilibria and linear programming algorithms.
• Abhinav Kumar, Microsoft Research, 6/2002 through 8/2002, 8/2003, and 6/2004 through 8/2004
  • Abhinav and I worked on several sphere packing problems and began collaborating on a paper on the Leech lattice (which we continued working on after his internship). More recently we have studied point configurations that minimize potential energy.
• Adam Smith, Microsoft Research, 6/2003 through 8/2003
  • Adam worked on several of his own problems, including anonymization of large geometric datasets and fuzzy fingerprinting.
• Scott Sheffield, Microsoft Research, 6/2001 through 8/2001
  • Scott worked on tilings and statistical mechanics. He proved some fundamental results about ribbon tilings, and also made some progress on his thesis.
• Jared Weinstein, Microsoft Research, 6/2001 through 8/2001
  • Jared studied some intriguing patterns in continued fractions, and proved a theorem explaining where they come from. Unfortunately, an equivalent result had already been published in 1999 by some other authors.
• Vis Taraz, MIT Summer Program in Undergraduate Research, 6/1998 through 8/1998
  • Vis worked on efficient construction of digital signature schemes.