Current teaching
Past teaching
18.701 (Algebra I) , MIT, Fall 2022
Number theory, PROMYS and PROMYS Europe , Summer 2022
18.S995 (Discrete Geometry) , MIT, Spring 2022
18.510 (Introduction to Mathematical Logic and Set Theory) , MIT, Fall 2021
Number theory, PROMYS and PROMYS Europe , Summer 2021
18.S096 (Ethics of Data) , taught with Mary L. Gray , MIT, Spring 2021
18.504 (Seminar in Logic) , MIT, Fall 2020
Undecidability and Hilbert's 10th Problem (with Cameron Freer), PROMYS , Summer 2020
18.821 (Project Laboratory in Mathematics) , MIT, Spring 2020
18.510 (Introduction to Mathematical Logic and Set Theory) , MIT, Fall 2019
Number theory, PROMYS and PROMYS Europe , Summer 2019
18.504 (Seminar in Logic) , MIT, Spring 2019
18.821 (Project Laboratory in Mathematics) , MIT, Fall 2018
Number theory, PROMYS and PROMYS Europe , Summer 2018
18.510 (Introduction to Mathematical Logic and Set Theory) , MIT, Fall 2017
Number theory, PROMYS and PROMYS Europe , Summer 2017
18.504 (Seminar in Logic) , MIT, Spring 2017
18.S995 (Applied Math for Pure Mathematicians), MIT, Fall 2016
Number theory, PROMYS and PROMYS Europe , Summer 2016
18.821 (Project Laboratory in Mathematics) , MIT, Spring 2016
18.510 (Introduction to Mathematical Logic and Set Theory), MIT, Fall 2015
Number theory, PROMYS and PROMYS Europe , Summer 2015
18.504 (Seminar in Logic), MIT, Spring 2015
18.S996 (Applied Math for Pure Mathematicians), MIT, Fall 2014
18.510 (Introduction to Mathematical Logic and Set Theory), MIT, Fall 2013
18.A34 (Mathematical Problem Solving), MIT, Fall 2013
18.504 (Seminar in Logic), MIT, Spring 2013
18.995 (Applied Math for Pure Mathematicians), MIT, Fall 2012
18.A34 (Mathematical Problem Solving), MIT, Fall 2012
18.510 (Introduction to Mathematical Logic and Set Theory), MIT, Fall 2011
18.504 (Seminar in Logic), MIT, Spring 2011
18.995 (Applied Math for Pure Mathematicians), MIT, Fall 2010
Combinatorics, PROMYS , Summer 2009
CIMPA-UNESCO-Philippines Research School on Semidefinite Programming in Algebraic Combinatorics, July 2009
EIDMA/DIAMANT minicourse, March 2008
Paradoxes and the Foundations of Mathematics, SIMUW , Summer 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 , Summer 2006
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 , Summer 2005
Theory of Equations, SIMUW , Summer 2004
Combinatorics, Summer Institute for Mathematics at the University of Washington (SIMUW), Summer 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 (PROMYS) 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
Ph.D advisees
Yichi Zhang, MIT, current student
James Hirst , MIT, Ph.D. received 9/2020
Dissertation: Coupling Sparse Models and Dense Extremal Problems
Gwen McKinley , MIT, Ph.D. received 6/2020
Dissertation: Probabilistic and Extremal Behavior in Graphs and Matrices
Jake Wellens , MIT, Ph.D. received 6/2020
Dissertation: Assorted Results in Boolean Function Complexity, Uniform Sampling and Clique Partitions of Graphs
Ganesh Ajjanagadde (jointly advised with Gregory Wornell), MIT, Ph.D. received 6/2020
Dissertation: Fourier Analysis on the Hypercube, the Coefficient Problem, and Applications
Stephanie Vance, University of Washington, Ph.D. received 6/2009
Dissertation: Lattices and Sphere Packings in Euclidean Space
Chris Hanusa , University of Washington, Ph.D. received 6/2005
Dissertation: A Gessel-Viennot-type Method for Cycle Systems and Applications to Aztec Pillows
Research students supervised
Malik Amir, Microsoft Reserch New England, 6/2022 through 8/2022
Rachana Madhukara, Microsoft Reserch New England, 6/2022 through 8/2022
Andrew Salmon, Microsoft Reserch New England, 6/2020 through 8/2020 and 6/2021 through 8/2021
Ganesh Ajjanagadde , Microsoft Research New England, 6/2019 through 8/2019
Julia Gaudio , Microsoft Research New England, 6/2019 through 8/2019
Kimberly Villalobos Carballo, Microsoft Research New England, 6/2018 through 8/2018
Samsara Counts , Microsoft Research New England, 6/2018 through 8/2018
Nina Zubrilina, Microsoft Research New England, 6/2018 through 8/2018
Nicholas Triantafillou , Microsoft Research New England, 6/2016 through 8/2016
Laszlo M. Lovasz , Microsoft Research New England, 6/2015 through 8/2015
Eric Naslund, Microsoft Research New England, 6/2015 through 8/2015 and 6/2017 through 8/2017
Yufei Zhao , Microsoft Research New England, 6/2010 through 8/2010, 6/2011 through 8/2011, 6/2013 through 8/2013, and 6/2014 through 8/2014
Matthew de Courcy-Ireland, Microsoft Research New England, 6/2014 through 8/2014
Gregory Minton , Microsoft Research New England, 6/2011 through 8/2011, 6/2012 through 8/2012, and 6/2013 through 8/2013
Forest Tong, MIT Undergraduate Research Opportunities Program, 6/2013 through 8/2013
Fan Wei, Microsoft Research New England, 6/2012 through 8/2012
Daniel Fremont, MIT Undergraduate Research Opportunities Program, 6/2012 through 8/2012
Nathan Kaplan , Microsoft Research New England, 9/2011 through 12/2011
Edinah Gnang , Microsoft Research New England, 6/2011 through 8/2011
Sonya Vohra, Microsoft Research New England, 6/2011 through 8/2011
Daniel Kane , Microsoft Research New England, 6/2010 through 8/2010
Nadia Heninger , Microsoft Research New England, 12/2009 through 2/2010 and 6/2010 through 8/2010
Swastik Kopparty , Microsoft Research New England, 6/2009 through 8/2009
Shubhangi Saraf , Microsoft Research New England, 6/2009 through 8/2009
Jeechul Woo, Microsoft Research New England, 8/2008 through 12/2008 and 6/2009 through 8/2009
Yakov Kerzhner, Microsoft Research, 6/2007 through 8/2007
Blair Sullivan , Microsoft Research, 6/2007 through 8/2007
Jeffrey Wang, Microsoft Research, 6/2007 through 8/2007
Bryden Cais , Microsoft Research, 6/2005 through 8/2005
Brandon Ballinger, University of Washington VIGRE program, 9/2004 through 6/2005
Noah Giansiracusa , University of Washington VIGRE program, 9/2004 through 6/2005
Elizabeth Kelly, University of Washington VIGRE program, 9/2004 through 6/2005
Jonathan Kelner , Microsoft Research, 6/2004 through 8/2004
Abhinav Kumar , Microsoft Research, 6/2002 through 8/2002, 8/2003, and 6/2004 through 8/2004
Adam Smith , Microsoft Research, 6/2003 through 8/2003
Scott Sheffield , Microsoft Research, 6/2001 through 8/2001
Jared Weinstein , Microsoft Research, 6/2001 through 8/2001
Vis Taraz, MIT Summer Program in Undergraduate Research, 6/1998 through 8/1998