Publications

Found 55 results
to appear
Cohn, Henry, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska. "Universal optimality of the E_8 and Leech lattices and interpolation formulas." Annals of Mathematics (to appear).
2022
Blasiak, Jonah, Henry Cohn, Joshua A. Grochow, Kevin Pratt, and Chris Umans. "Matrix multiplication via matrix groups." Preprint (2022).
2021
Borgs, Christian, Jennifer T. Chayes, Henry Cohn, and Shirshendu Ganguly. "Consistent nonparametric estimation for heavy-tailed sparse graphs." Ann. Statist. 49 (2021): 1904-1930.
Cohn, Henry, and Nicholas Triantafillou. "Dual linear programming bounds for sphere packing via modular forms." Math. Comp. 91 (2021): 491-508.
Afkhami-Jeddi, Nima, Henry Cohn, Thomas Hartman, and Amirhossein Tajdini. "Free partition functions and an averaged holographic duality." J. High Energy Phys. (2021): Paper No. 130, 42 pages.
Cohn, Henry, and Andrew Salmon. "Sphere packing bounds via rescaling." Preprint (2021).
2020
Afkhami-Jeddi, Nima, Henry Cohn, Thomas Hartman, David de Laat, and Amirhossein Tajdini. "High-dimensional sphere packing and the modular bootstrap." J. High Energy Phys. (2020): Paper No. 66, 44 pages.
2019
Borgs, Christian, Jennifer T. Chayes, Henry Cohn, and László Miklós Lovász. "Identifiability for graphexes and the weak kernel metric." In Building Bridges II, 29-157. Bolyai Soc. Math. Stud. Springer, Berlin, 2019.
Borgs, Christian, Jennifer T. Chayes, Henry Cohn, and Yufei Zhao. "An L^p theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions." Trans. Amer. Math. Soc. 372 (2019): 3019-3062.
Cohn, Henry, and Felipe Gonçalves. "An optimal uncertainty principle in twelve dimensions via modular forms." Invent. Math. 217 (2019): 799-831.
Borgs, Christian, Jennifer T. Chayes, Henry Cohn, and Victor Veitch. "Sampling perspectives on sparse exchangeable graphs." Ann. Probab. 47 (2019): 2754-2800.
2018
Cohn, Henry, and Matthew de Courcy-Ireland. "The Gaussian core model in high dimensions." Duke Math. J. 167 (2018): 2417-2455.
Borgs, Christian, Jennifer T. Chayes, Henry Cohn, and Yufei Zhao. "An L^p theory of sparse graph convergence II: LD convergence, quotients and right convergence." Ann. Probab. 46 (2018): 337-396.
2017
Blasiak, Jonah, Thomas Church, Henry Cohn, Joshua A. Grochow, Eric Naslund, William F. Sawin, and Chris Umans. "On cap sets and the group-theoretic approach to matrix multiplication." Discrete Anal. (2017): Paper No. 3, 27 pages.
Cohn, Henry. "A conceptual breakthrough in sphere packing." Notices Amer. Math. Soc. 64 (2017): 102-115.
Cohn, Henry. "Packing, coding, and ground states." In Mathematics and materials, 45-102. IAS/Park City Math. Ser. Amer. Math. Soc., Providence, RI, 2017.
Borgs, Christian, Jennifer T. Chayes, Henry Cohn, and Nina Holden. "Sparse exchangeable graphs and their limits via graphon processes." J. Mach. Learn. Res. 18 (2017): Paper No. 210, 71 pages.
Cohn, Henry, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska. "The sphere packing problem in dimension 24." Ann. of Math. (2) 185 (2017): 1017-1033.
Blasiak, Jonah, Thomas Church, Henry Cohn, Joshua A. Grochow, and Chris Umans. "Which groups are amenable to proving exponent two for matrix multiplication?" Preprint (2017).
2016
Cohn, Henry, Abhinav Kumar, and Gregory Minton. "Optimal simplices and codes in projective spaces." Geom. Topol. 20 (2016): 1289-1357.
Cohn, Henry, and Stephen D. Miller. "Some properties of optimal functions for sphere packing in dimensions 8 and 24." Preprint (2016).
2015
Cohn, Henry, and Nadia Heninger. "Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding." Adv. Math. Commun. 9 (2015): 311-339.
Cohn, Henry, and Abhinav Kumar. "Metacommutation of Hurwitz primes." Proc. Amer. Math. Soc. 143 (2015): 1459-1469.
2014
Cohn, Henry, and Yufei Zhao. "Energy-minimizing error-correcting codes." IEEE Trans. Inform. Theory 60 (2014): 7442-7450.
Cohn, Henry, Abhinav Kumar, Christian Reiher, and Achill Schürmann. "Formal duality and generalizations of the Poisson summation formula." In Discrete geometry and algebraic combinatorics, 123-140. Contemp. Math. Amer. Math. Soc., Providence, RI, 2014.
Bitansky, Nir, Ran Canetti, Henry Cohn, Shafi Goldwasser, Yael Tauman Kalai, Omer Paneth, and Alon Rosen. "The impossibility of obfuscation with auxiliary input or a universal simulator." In Advances in Cryptology–-CRYPTO 2014, 71-89. Lecture Notes in Comput. Sci. Springer, Heidelberg, 2014.
Cohn, Henry, and Yufei Zhao. "Sphere packing bounds via spherical codes." Duke Math. J. 163 (2014): 1965-2002.
2013
Cohn, Henry, and Nadia Heninger. "Approximate common divisors via lattices." In ANTS X–-Proceedings of the Tenth Algorithmic Number Theory Symposium, 271-293. Open Book Ser. Math. Sci. Publ., Berkeley, CA, 2013.
Cohn, Henry, and Christopher Umans. "Fast matrix multiplication using coherent configurations." In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, 1074-1087. SIAM, Philadelphia, PA, 2013.
2012
Arnold, Douglas N., and Henry Cohn. "Mathematicians take a stand." Notices Amer. Math. Soc. 59 (2012): 828-833.
Cohn, Henry, and Jeechul Woo. "Three-point bounds for energy minimization." J. Amer. Math. Soc. 25 (2012): 929-958.
2011
Cohn, Henry, Yang Jiao, Abhinav Kumar, and Salvatore Torquato. "Rigidity of spherical codes." Geom. Topol. 15 (2011): 2235-2273.
2010
Cohn, Henry. "Order and disorder in energy minimization." In Proceedings of the International Congress of Mathematicians, Hyderabad, August 19–27, 2010, Volume IV, 2416-2443. Hindustan Book Agency, New Delhi, 2010.
Cohn, Henry, Noam D. Elkies, Abhinav Kumar, and Achill Schürmann. "Point configurations that are asymmetric yet balanced." Proc. Amer. Math. Soc. 138 (2010): 2863-2872.
2009
Cohn, Henry, and Abhinav Kumar. "Algorithmic design of self-assembling structures." Proc. Natl. Acad. Sci. USA 106 (2009): 9570-9575.
Ballinger, Brandon, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, and Achill Schürmann. "Experimental study of energy-minimizing point configurations on spheres." Experiment. Math. 18 (2009): 257-283.
Cohn, Henry, Abhinav Kumar, and Achill Schürmann. "Ground states and formal duality relations in the Gaussian core model." Phys. Rev. E (3) 80 (2009): 061116.
Cohn, Henry, and Abhinav Kumar. "Optimality and uniqueness of the Leech lattice among lattices." Ann. of Math. (2) 170 (2009): 1003-1050.
2008
Cohn, Henry, and Abhinav Kumar. "Counterintuitive ground states in soft-core models." Phys. Rev. E (3) 78 (2008): 061113.
2007
Cohn, Henry, John H. Conway, Noam D. Elkies, and Abhinav Kumar. "The D_4 root system is not universally optimal." Experiment. Math. 16 (2007): 313-320.
Cohn, Henry, and Abhinav Kumar. "Uniqueness of the (22,891,1/4) spherical code." New York J. Math. 13 (2007): 147-157.
Cohn, Henry, and Abhinav Kumar. "Universally optimal distribution of points on spheres." J. Amer. Math. Soc. 20 (2007): 99-148.
2006
Cohn, Henry. "A short proof of the simple continued fraction expansion of e." Amer. Math. Monthly 113 (2006): 57-62.
2005
Cohn, Henry, Robert Kleinberg, Balázs Szegedy, and Christopher Umans. "Group-theoretic algorithms for matrix multiplication." In Proceedings of the 46th Annual Symposium on Foundations of Computer Science, 379-388. IEEE Computer Society, 2005.
2004
Cohn, Henry, and Abhinav Kumar. "The densest lattice in twenty-four dimensions." Electron. Res. Announc. Amer. Math. Soc. 10 (2004): 58-67.
Cohn, Henry. "Projective geometry over F_1 and the Gaussian binomial coefficients." Amer. Math. Monthly 111 (2004): 487-495.
2003
Cohn, Henry, and Christopher Umans. "A group-theoretic approach to fast matrix multiplication." In Proceedings of the 44th Annual Symposium on Foundations of Computer Science, 438-449. IEEE Computer Society, 2003.
Cohn, Henry, and Noam Elkies. "New upper bounds on sphere packings I." Ann. of Math. (2) 157 (2003): 689-714.
2002
Cohn, Henry, Robin Pemantle, and James Propp. "Generating a random sink-free orientation in quadratic time." Electron. J. Combin. 9 (2002): Research Paper 10, 13 pages.
Cohn, Henry. "New upper bounds on sphere packings II." Geom. Topol. 6 (2002): 329-353.
2001
Cohn, Henry, Richard Kenyon, and James Propp. "A variational principle for domino tilings." J. Amer. Math. Soc. 14 (2001): 297-346.
1999
Cohn, Henry. "2-adic behavior of numbers of domino tilings." Electron. J. Combin. 6 (1999): Research Paper 14, 7 pages.
1998
Cohn, Henry, Michael Larsen, and James Propp. "The shape of a typical boxed plane partition." New York J. Math. 4 (1998): 137-165.
1996
Cohn, Henry, Noam Elkies, and James Propp. "Local statistics for random domino tilings of the Aztec diamond." Duke Math. J. 85 (1996): 117-166.
Cohn, Henry. "Symmetry and specializability in continued fractions." Acta Arith. 75 (1996): 297-320.