### Expository Addresses, Talks, and Presentations

Plenary:

Educational:

At the Harvard Math Table:

 "Lattice Theory for the Working Matchmaker," October 7, 2014: A survey of the theory and practical applications of generalized matching, focusing on fixed-point characterizations, lattice structure theorems, and cadet--branch matching. "Large Games IV: A New Hope," November 16, 2010: A proof of Bodoh-Creed's "Death Star" of a theorem on the approximation of large economies by continua. "The Rap Battle of the Millennium," May 5, 2009: Zachary Abel and I rap our way through the seven Clay Mathematics Institute Millennium Prize Problems in the first-ever "sung through" math table lecture. "Koch's Condition on Type II Codes of Length 24," April 14, 2009: An introduction to binary linear codes and harmonic weight enumerators, with an application to a theorem of Koch on the possible tetrad systems of Type II codes of length 24. "Who wants to be a Math Concentrator?," March 17, 2009: A panel of current mathematics concentrators advising prospective concentrators in mathematics and related fields. "Matchmaker, Matchmaker, Clear Out My House," November 11, 2008: A thirty-minute course in the theory of matching, introducing the marriage and college admissions problems, the Gale-Shapley algorithm, unraveling, and generalized matching. "C=15," October 30, 2007 (awarded the top Robert Fletcher Rogers Prize): A discussion of recent results in quadratic form representation theory, focusing on the Conway-Schneeberger "Fifteen Theorem," the Bhargava-Hanke "290 Theorem," and Kim, Kim, and Oh's criterion results for representations of higher-rank forms. "Opetopia," November 21, 2006: An introduction to the theory and applications of $n$-categories, focusing especially on the "opetopic" realization of $n$-category theory. "Metric-Preserving Functions," February 21, 2006: An introduction to the theory of metric-preserving functions, those functions $f:[0,\infty)\to[0,\infty)$ such that for any metric space $X$ with metric $d$, $f\circ d$ is a metric on $X$.

Panel Presentations:

• Harvard Undergraduate Economics Association, October 26, 2009.