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

Affiliations: Harvard Center of Mathematical Sciences and Applications (2015-present), Harvard Program for Evolutionary Dynamics (2012-2016), 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)

Grants and Fellowships: AMS-Simons Travel Grant (2011-2014), 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: Center for Excellence in Education Alumni Award for Outstanding Achievement in STEM and Business (2013), St. Mark's Institute of Mathematics Great Math Challenge Award [with P. M. Kominers] (2010), 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 Papers:

• Weighted Generating Functions and Configuration Results for Type II Lattices and Codes. (Undergraduate thesis, (2009).) (Awarded the Thomas Temple Hoopes Prize.)
• Configurations of Extremal Type II Codes via Harmonic Weight Enumerators [with N. D. Elkies]. (Journal de Theorie des Nombres de Bordeaux 31(3), (2019), pp. 679-688.) (Preprint.)
• Complete Characterization of the Schulze-Pillot Lattice with an SL2(Z/71Z) Action [with N. D. Elkies and Z. Abel]. (In preparation.)
• Weighted Generating Functions for Type II Lattices and Codes [with N. D. Elkies]. (Quadratic and Higher Degree Forms (ed. Krishnaswami Alladi, Manjul Bhargava, David Savitt, and Pham Huu Tiep), Developments in Mathematics 31, Springer, (2013), pp. 63-108.) (Preprint.)
• Minimal S-Universality Criteria May Vary in Size [with N. D. Elkies and D. M. Kane]. (Journal de Theorie des Nombres de Bordeaux 23(3), (2013), pp. 557-563.) (Preprint.)
• Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions [with D. M. Kane]. (Canadian Mathematical Bulletin 57(3), (2014), pp. 551-561.) (Preprint.)
• 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.)
• On Congruence Conditions for Primality [with S. Gong]. (INTEGERS: The Electronic Journal of Combinatorial Number Theory 10(3), (2010), pp. 313–317.)
• Oh's 8-universality Criterion is Unique. (Forthcoming, Kyungpook Mathematical Journal.)
• 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. (Note di Matematica 28(2), (2008), pp. 203-206.)
• Configurations of Extremal Even Unimodular Lattices. (International Journal of Number Theory 5(3), (2009), pp. 457-464.) (Preprint.)

Discrete Mathematics Papers:

• Prisoners, Rooms, and Lightswitches [with D. M. Kane]. (Electronic Journal of Combinatorics 28(1), (2021), P1.27.) (Preprint.)
• A Constant Bound for the Periods of Parallel Chip-firing Games with Many Chips [with P. M. Kominers]. (Archiv der Mathematik 95(1), (2010), pp. 9-13.) (Preprint.) (Recognized in the St. Mark's Institute of Mathematics Great Math Challenge.)

Computational Geometry Papers:

• 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), pp. 1045-1064.)
• 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]. (Graphs and Combinatorics 27(1), (2011), pp. 47-60.) (Extended abstract, Proceedings of the 21st Canadian Conference on Computational Geometry, (2009).) (Preprint.)
• Universal Reconfiguration of (Hyper-)cubic Robots [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]. (Discrete & Computational Geometry 47(1), (2012), pp. 150-186.) (Conference paper, Proceedings of the 24th Annual Symposium on Computational Geometry, (2008), pp. 110-119.) (Preprint.)

Other Papers:

• A Categorical Construction of Ultrafilters [with D. Litt and Z. Abel]. (Rocky Mountain Journal of Mathematics 40(5), (2010), pp. 1611-1617.) (Preprint.)

Short Articles:

• Fractal Flipbooks [with A. Hawksley]. (Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, (2016), pp. 615-620.)
• Flipbook Polyhedra [with A. Hawksley]. (Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, (2013), pp. 619-624.)
• Irrational Roots Revisited. (Note 94.16, The Mathematical Gazette 94(530), (2010), p. 28.)
• Improved Bounds on the Sizes of S.P Numbers [with P. M. Kominers]. (Note 94.05, The Mathematical Gazette 94(529), (2010), pp. 127-129.)
• Walk versus Wait: The Lazy Mathematician Wins [with J. G. Chen and R. W. Sinnott]. (Preprint.)
• Finding Matrices that Satisfy Functional Equations. (College Mathematics Journal, 40(4), (2009), pp. 289-292.) (Preprint, abstract.)

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, Vida Dujmovic, Noam D. Elkies, Robin Flatland, Sherry Gong, Andrea Hawksley, Shaofang Hong, Ferran Hurtado, Daniel M. Kane, Paul M. Kominers, Stefan Langerman, Daniel Litt, Attila Por, Robert Schweller, Robert W. Sinnott, David R. Wood