Henry Cohn's research publications

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This page links to all my research papers (my non-research publications can be found here). The icons on the left let you read the abstract or download the paper in PDF format. The abstract page also links to other formats.

I tend to put papers on the web only when they are essentially complete. If you would like to see the current version of a draft manuscript you don't see here or some work in progress, just let me know. Another thing I'm not currently posting here are lecture slides and course notes. They aren't designed to stand on their own, so they are of interest primarily to people who were there. If you were there and want a copy (or weren't there and want to see what you missed), send me e-mail and I'll send you a link.

I've organized the papers here by topic rather than date, since that seems most useful. Here is a full list in roughly chronological order.

Sphere Packing:

		New upper bounds on sphere packings I (with Noam Elkies) Annals of Mathematics 157 (2003), 689-714, arXiv:math.MG/0110009
		New upper bounds on sphere packings II Geometry and Topology 6 (2002), 329-353, arXiv:math.MG/0110010
		The densest lattice in twenty-four dimensions (with Abhinav Kumar) Electronic Research Announcements of the American Mathematical Society 10 (2004), 58-67, arXiv:math.MG/0408174
		Uniqueness of the (22,891,1/4) spherical code (with Abhinav Kumar) New York Journal of Mathematics 13 (2007), 147-157, arXiv:math.MG/0607448
		Optimality and uniqueness of the Leech lattice among lattices (with Abhinav Kumar) Annals of Mathematics 170 (2009), 1003-1050, arXiv:math.MG/0403263
		Rigidity of spherical codes (with Yang Jiao, Abhinav Kumar, and Sal Torquato) Geometry and Topology 15 (2011), 2235-2273, arXiv:1102.5060
		Sphere packing bounds via spherical codes (with Yufei Zhao) preprint, 2012, arXiv:1212.5966

Potential Energy Minimization:

		Universally optimal distribution of points on spheres (with Abhinav Kumar) Journal of the American Mathematical Society 20 (2007), 99-148, arXiv:math.MG/0607446
		The D_4 root system is not universally optimal (with John Conway, Noam Elkies, and Abhinav Kumar) Experimental Mathematics 16 (2007), 313-320, arXiv:math.MG/0607447
		Counterintuitive ground states in soft-core models (with Abhinav Kumar) Physical Review E 78 (2008), 061113, arXiv:0811.1236
		Experimental study of energy-minimizing point configurations on spheres (with Brandon Ballinger, Greg Blekherman, Noah Giansiracusa, Elizabeth Kelly, and Achill Schürmann) Experimental Mathematics 18 (2009), 257-283, arXiv:math.MG/0611451
		Ground states and formal duality relations in the Gaussian core model (with Abhinav Kumar and Achill Schürmann) Physical Review E 80 (2009), 061116, arXiv:0911.2169
		Point configurations that are asymmetric yet balanced (with Noam Elkies, Abhinav Kumar, and Achill Schürmann) Proceedings of the American Mathematical Society 138 (2010), 2863-2872, arXiv:0812.2579
		Order and disorder in energy minimization Proceedings of the International Congress of Mathematicians, Hyderabad, August 19-27, 2010, Volume IV, pages 2416-2443, Hindustan Book Agency, New Delhi, 2010, arXiv:1003.3053
		Three-point bounds for energy minimization (with Jeechul Woo) Journal of the American Mathematical Society 25 (2012), 929-958, arXiv:1103.0485

		Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding (with Nadia Heninger) preprint, 2010 (extended abstract was published in proceedings of ICS 2011), arXiv:1008.1284
		Approximate common divisors via lattices (with Nadia Heninger) to appear in Proceedings of ANTS 2012, arXiv:1108.2714

Fast Matrix Multiplication:

		A group-theoretic approach to fast matrix multiplication (with Chris Umans) Proceedings of the 44th Annual Symposium on Foundations of Computer Science (11-14 October 2003, Cambridge, MA), IEEE Computer Society, pp. 438-449, arXiv:math.GR/0307321
		Group-theoretic algorithms for matrix multiplication (with Bobby Kleinberg, Balazs Szegedy, and Chris Umans) Proceedings of the 46th Annual Symposium on Foundations of Computer Science (23-25 October 2005, Pittsburgh, PA), IEEE Computer Society, pp. 379-388, arXiv:math.GR/0511460
		Fast matrix multiplication using coherent configurations (with Chris Umans) Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (6-8 January 2013, New Orleans, LA), Society for Industrial and Applied Mathematics, pp. 1074-1087, arXiv:1207.6528

Random Tilings and the Dimer Model:

		Local statistics for random domino tilings of the Aztec diamond (with Noam Elkies and Jim Propp) Duke Mathematical Journal 85 (1996), 117-166, arXiv:math.CO/0008243
		The shape of a typical boxed plane partition (with Michael Larsen and Jim Propp) New York Journal of Mathematics 4 (1998), 137-165, arXiv:math.CO/9801059
		A variational principle for domino tilings (with Rick Kenyon and Jim Propp) Journal of the American Mathematical Society 14 (2001), 297-346, arXiv:math.CO/0008220

		Symmetry and specializability in continued fractions Acta Arithmetica 75.4 (1996), 297-320, arXiv:math.NT/0008221
		2-adic behavior of numbers of domino tilings Electronic Journal of Combinatorics 6 (1999), #R14, arXiv:math.CO/0008222
		A short proof of the simple continued fraction expansion of e American Mathematical Monthly 113 (2006), 57-62, arXiv:math.NT/0601660