Research Interests: Quadratic form representation theory, Even unimodular lattices, Modular forms, Computational geometry, Category theory

Affiliations: Duluth Undergraduate Research Program (honorary, 2010), Center for Excellence in Education Research Science Institute (RSI) (2004-present), Harvard University Department of Mathematics (2005-2009), Harvard College Program for Research in Science and Engineering (PRISE) (2006; 2008)

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)

Awards: AMS-MAA-SIAM Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student (2010), Thomas Temple Hoopes Prize (2009), First Place Robert Fletcher Rogers Prize (2008), First Place American Mathematical Society Karl Menger Prize (2005)

Number Theory Projects:

• Weighted Generating Functions and Configuration Results for Type II Lattices and Codes. (Undergraduate thesis, (2009).) (Awarded the Thomas Temple Hoopes Prize.)
• A New Development of Harmonic Weight Enumerators [with N. D. Elkies]. (In preparation.)
• Complete Characterization of the Schulze-Pillot Lattice with an SL2(Z/71Z) Action [with N. D. Elkies and Z. Abel]. (In preparation.)
• Extremality of the Schulze-Pillot Lattice with an SL2(Z/79Z) Action [with Z. Abel, S. Donnelly, N. D. Elkies, D. Stehle, and M. Watkins]. (In preparation.) (Extended abstract, Explicit Methods in Number Theory, Mathematisches Forschungsinstitut Oberwolfach (33), (2009).)
• Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions, II [with D. M. Kane]. (Preprint available upon request.)
• Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80 [with N. D. Elkies]. (Proceedings of the American Mathematical Society 138(1), (2010), pp. 105-108.) (Preprint.)
• On the Classification of Type II Codes of Length 24 [with N. D. Elkies]. (SIAM Journal on Discrete Mathematics 23(4), (2010), pp. 2173-2177.) (Preprint.)
• Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions [with S. Hong]. (Proceedings of the American Mathematical Society 138(3), (2010), pp. 809-813.) (Preprint.)
• The 8-universality Criterion is Unique. (Preprint.)
• On Universal Binary Hermitian Forms. (INTEGERS: The Electronic Journal of Combinatorial Number Theory 9, (2009), #A2. {Zbl pre05551206.}) (Preprint.)
• Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3) [with Z. Abel]. (Journal de Theorie des Nombres de Bordeaux 20(2), (2008), pp. 365-371. {Zbl pre05543167.}) (Abstract, preprint.)
• Uniqueness of the 2-universality Criterion. (Forthcoming, Note di Matematica.)
• Configurations of Extremal Even Unimodular Lattices. (International Journal of Number Theory 5(3), (2009), pp. 457-464.) (Preprint.)

Computational Geometry Projects:

• Shape Replication Through Self-Assembly and RNase Enzymes [with Z. Abel, N. Benbernou, M. Damian, E. D. Demaine, R. Flatland, R. Schweller, and M. L. Demaine]. (Proceedings of the 2010 ACM-SIAM Symposium on Discrete Algorithms, (2010).)
• Every Large Point Set contains Many Collinear Points or an Empty Pentagon [with Z. Abel, B. Ballinger, P. Bose, S. Collette, V. Dujmovic, F. Hurtado, S. Langerman, A. Por, and D. R. Wood]. (Preprint.) (Extended abstract, Proceedings of the 21st Canadian Conference on Computational Geometry, (2009).)
• Pushing Hypercubes Around [with Z. Abel]. (Preprint, under revision.)
• 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, (2008), pp. 110-119. {Zbl pre05507856.}) (Preprint.)

Other Projects:

• A Constant Bound for the Periods of Parallel Chip-firing Games with Many Chips [with P. M. Kominers]. (Forthcoming, Archiv der Mathematik.) (Originally circulated as Candy-passing Games on General Graphs, II.)
• A Categorical Construction of Ultrafilters [with D. Litt and Z. Abel]. (Forthcoming, Rocky Mountain Journal of Mathematics.)

Short Articles:

• On Congruence Conditions for Primality [with S. Gong]. (Forthcoming, INTEGERS: The Electronic Journal of Combinatorial Number Theory.)
• Irrational Roots Revisited. (Forthcoming, The Mathematical Gazette, (2010).)
• Improved Bounds on the Sizes of S.P Numbers [with P. M. Kominers]. (Forthcoming, The Mathematical Gazette, (2010).)
• Walk versus Wait: The Lazy Mathematician Wins [with J. G. Chen and R. W. Sinnott]. (Preprint.)
• Finding Matrices Which Satisfy Functional Equations. (College Mathematics Journal, 40(4), (2009), pp. 289-292.)

Comments:

• A correspondence note on Myerson's 'Irrationality via Well-ordering'. (Gazette of the Australian Mathematical Society 36(1), (2009), p. 53.)

Expository Articles:

• Perelman, Poincare, and the Ricci Flow. (Unpublished.)

Collaborators: Timothy G. Abbott, Zachary Abel, Brad Ballinger, Nadia Benbernou, Prosenjit Bose, David Charlton, Justin G. Chen, Sebastien Collette, Mirela Damian, Erik D. Demaine, Martin L. Demaine, Steve Donnelly, Vida Dujmovic, Noam D. Elkies, Robin Flatland, Sherry Gong, Shaofang Hong, Ferran Hurtado, Daniel M. Kane, Paul M. Kominers, Stefan Langerman, Daniel Litt, Attila Por, Robert Schweller, Robert W. Sinnott, Damien Stehle, Mark Watkins, David R. Wood