Research

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Mathematics

• Research Interests: Quadratic form representation theory, Even unimodular lattices, Modular forms, Computational geometry, Category theory
  
  
• Complete Characterization of the Unique Even Unimodular Lattice Invariant under SL2(Z/71Z) [with N. D. Elkies and Z. Abel]. (In preparation.)
• The 8-universality Criterion is Unique. (Preprint.)
• Pushing Hypercubes Around [with Z. Abel]. (Preprint.)
• On Universal Binary Hermitian Forms. (Preprint.)
• Hinged Dissections Exist [with T. Abbott, Z. Abel (corresponding author), D. Charlton, E. D. Demaine, and M. L. Demaine]. (Proceedings of the 24th Annual Symposium on Computational Geometry, pp. 110-119.) (Preprint, arXiv:0712.2094.)
• A Categorical Construction of Ultrafilters [with D. Litt and Z. Abel]. (Preprint.)
• Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3) [with Z. Abel]. (To appear, Journal de Theorie des Nombres de Bordeaux.)
• Uniqueness of the 2-universality Criterion. (To appear, Note di Matematica 28(2), (2008).)
• Configurations of Extremal Even Unimodular Lattices. (To appear, International Journal of Number Theory.)
  
  
• Short Articles
  • Improved Bounds on the Sizes of S.P Numbers [with P. M. Kominers]. (Preprint.)
  • Walk versus Wait: The Lazy Mathematician Wins [with J. G. Chen and R. W. Sinnott]. (Preprint.)
  • Finding Matrices Which Satisfy Functional Equations. (Preprint available upon request.)
  
  
• Expository Articles
  • Universal Forms: The Fifteen Theorem and its Generalizations (Preprint available upon request.)
  • Perelman, Poincare, and the Ricci Flow. (To appear, PRISE Journal 1, (2008).)
  
  
• Collaborators: Timothy G. Abbott, Zachary Abel, David Charlton, Justin G. Chen, Eric D. Demaine, Martin L. Demaine, Noam D. Elkies, Paul M. Kominers, Daniel Litt, Christopher C. Mihelich, Robert W. Sinnott
  
  
• Fellowships: Harvard Mathematics Department Highbridge Fellowship (2008), Harvard College Program for Research in Science and Engineering Fellowship (2006), Center for Excellence in Education Research Science Institute Summer Scholarship (2004)

Economics

• Research Interests: Mathematical economics, Agglomeration, Mechanism design, Economics of entry, Law and economics, Urban economics, Operations research
  
  
• Social Interactions and Innovation
• A Concentration-Based Index of Industrial Agglomeration [with B. Harrison]. (Working paper available, upon request.)
• Gender Inequality in Social Contexts [with D. L. Chen and C. Jenq]. (In progress.)
• Salary Erosion and Federal Judicial Resignation. (Working paper.)
  
  
• Short Articles
  • Response to May 2007 article by Frank Giarratani, Gene Gruver, & Randall Jackson on Industry Agglomeration. (Economic Development Quarterly.)
  
  
• Expository Articles
  • Measuring Agglomeration. (To appear, The Harvard Economist.)
  
  
• Research Assistanceships
  • Prof. Edward L. Glaeser, Harvard University Department of Economics and Harvard Kennedy School, (2007-present)
    • Did the Death of Distance Hurt Detroit and Help New York?
    • Housing Dynamics
    • Housing Supply and Housing Bubbles
  • Prof. Andrei Shleifer, Harvard University Department of Economics, (2008-present)
  • Prof. Susan Athey, Harvard University Department of Economics, (2008-present)
  • Position Auctions with Consumer Search
  • Prof. William R. Kerr, Harvard Business School, (2008-present)
  
  
• Collaborators: Daniel Li Chen, Brett Harrison, Christina Jenq
  
  
• Fellowships: Harvard Institute for Quantitative Social Science Summer Research Scholars Program Fellowship (2008), Harvard College Program for Research in Science and Engineering Program Assistant Fellowship (2008)

Musicology

• Research Interests: Musical notation systems, Historical ethnomusicology, Leonard Bernstein
  
  
• Pied Pipers and Prokofiev: A Musical Ethnography of Children's Literature (Working paper available upon request.)
• Textual Expression in Gregorian Chant: A Computer-assisted Study. (Working paper available upon request.)
• Leonard Bernstein's Doodles: Reading Outside the Lines at the Library of Congress. (To appear, Journal of the Society for American Music.) (Originally presented as "Leonard Bernstein's Doodles: Grasping Genius Through Graphology" at Leonard Bernstein, Boston to Broadway: Concerts and Symposia at Harvard University, October 14, 2006.)
  
  
• Fellowships: Research Support from the Harvard University Department of Music (2006)

See also a list of my research publications and talks.