Teaching

Current teaching

• 18.S096 (Discrete Geometry), MIT, Spring 2025

Past teaching

• 18.03 (Differential Equations), MIT, Fall 2024
• Number theory, PROMYS and PROMYS Europe, Summer 2024
• 18.S096 (Seminar in Probability Theory), MIT, Spring 2024
• 18.510 (Introduction to Mathematical Logic and Set Theory), MIT, Fall 2023
• Number theory, PROMYS and PROMYS Europe, Summer 2023
• 18.504 (Seminar in Logic), MIT, Spring 2023
• 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, Ph.D. received 9/2022
  • Dissertation: A Solution of the Energy Minimization Problem for Codes of Codimension 1
• 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

• Alex Cohen, Microsoft Reserch New England, 6/2024 through 8/2024
• Anqi Li, Microsoft Reserch New England, 6/2023 through 8/2023
• 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