2025
Jonah Blasiak, Henry Cohn, Joshua A. Grochow, Kevin Pratt, and Chris Umans, Finite matrix multiplication algorithms from infinite groups, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025), Leibniz International Proceedings in Informatics (LIPIcs), vol. 325, Schloss Dagstuhl — Leibniz-Zentrum für Informatik, 2025, pp. 18:1–18:23, doi:10.4230/LIPIcs.ITCS.2025.18, arXiv:2410.14905.
2024
Henry Cohn, David de Laat, and Nando Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
Henry Cohn and Anqi Li, Improved kissing numbers in seventeen through twenty-one dimensions, preprint, 2024, arXiv:2411.04916.
Henry Cohn and Isaac Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937.
Henry Cohn, From sphere packing to Fourier interpolation, Bull. Amer. Math. Soc. (N.S.) 61 (2024), no. 1, 3–22, doi:10.1090/bull/1813, arXiv:2407.14999.
Dan Abramovich, Henry Cohn, David Futer, and Robert Harington, Double-anonymous peer review in mathematics: implementation for American Mathematical Society journals, Notices Amer. Math. Soc. 71 (2024), no. 8, 1079–1081, doi:10.1090/noti3013.
Henry Cohn, Dingding Dong, and Felipe Gonçalves, Sign uncertainty principles and low-degree polynomials, Proc. Amer. Math. Soc. Ser. B 11 (2024), 224–228, doi:10.1090/bproc/219, arXiv:2210.01684.
2023
Henry Cohn, The work of Maryna Viazovska, Proceedings of the International Congress of Mathematicians, July 6–14, 2022, Volume 1, EMS Press, 2023, pp. 82–105, doi:10.4171/ICM2022/213, arXiv:2207.06913.
Jonah Blasiak, Henry Cohn, Joshua A. Grochow, Kevin Pratt, and Chris Umans, Matrix multiplication via matrix groups, 14th Innovations in Theoretical Computer Science Conference, LIPIcs. Leibniz Int. Proc. Inform., vol. 251, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2023, Art. No. 19, 16, doi:10.4230/lipics.itcs.2023.19, arXiv:2204.03826.
Gail Burrill, Henry Cohn, Yvonne Lai, Dev P. Sinha, Ji Y. Son, and Katherine F. Stevenson, Listening for common ground in high school and early collegiate mathematics, Notices Amer. Math. Soc. 70 (2023), no. 5, 798–805, doi:10.1090/noti2689.
2022
Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska, Universal optimality of the E8 and Leech lattices and interpolation formulas, Ann. of Math. (2) 196 (2022), no. 3, 983–1082, doi:10.4007/annals.2022.196.3.3, arXiv:1902.05438.
Henry Cohn, David de Laat, and Andrew Salmon, Three-point bounds for sphere packing, preprint, 2022, arXiv:2206.15373.
2021
Henry Cohn and Andrew Salmon, Sphere packing bounds via rescaling, preprint, 2021, arXiv:2108.10936.
Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartman, and Amirhossein Tajdini, Free partition functions and an averaged holographic duality, J. High Energy Phys. (2021), no. 1, Paper No. 130, 42 pages, doi:10.1007/jhep01(2021)130, arXiv:2006.04839.
Christian Borgs, Jennifer T. Chayes, Henry Cohn, and Shirshendu Ganguly, Consistent nonparametric estimation for heavy-tailed sparse graphs, Ann. Statist. 49 (2021), no. 4, 1904–1930, doi:10.1214/20-aos1985, arXiv:1508.06675.
Henry Cohn and Nicholas Triantafillou, Dual linear programming bounds for sphere packing via modular forms, Math. Comp. 91 (2021), no. 333, 491–508, doi:10.1090/mcom/3662, arXiv:1909.04772.
2020
Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartman, David de Laat, and Amirhossein Tajdini, High-dimensional sphere packing and the modular bootstrap, J. High Energy Phys. (2020), no. 12, Paper No. 66, 44 pages, doi:10.1007/jhep12(2020)066, arXiv:2006.02560.
2019
Henry Cohn and Felipe Gonçalves, An optimal uncertainty principle in twelve dimensions via modular forms, Invent. Math. 217 (2019), no. 3, 799–831, doi:10.1007/s00222-019-00875-4, arXiv:1712.04438.
Christian Borgs, Jennifer T. Chayes, Henry Cohn, and Victor Veitch, Sampling perspectives on sparse exchangeable graphs, Ann. Probab. 47 (2019), no. 5, 2754–2800, doi:10.1214/18-AOP1320, arXiv:1708.03237.
Christian Borgs, Jennifer T. Chayes, Henry Cohn, and Yufei Zhao, An Lp theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions, Trans. Amer. Math. Soc. 372 (2019), no. 5, 3019–3062, doi:10.1090/tran/7543, arXiv:1401.2906.
Christian Borgs, Jennifer T. Chayes, Henry Cohn, and László Miklós Lovász, Identifiability for graphexes and the weak kernel metric, Building Bridges II, Bolyai Soc. Math. Stud., no. 28, Springer, Berlin, 2019, pp. 29–157, doi:10.1007/978-3-662-59204-5_3, arXiv:1804.03277.
2018
Henry Cohn and Matthew de Courcy-Ireland, The Gaussian core model in high dimensions, Duke Math. J. 167 (2018), no. 13, 2417–2455, doi:10.1215/00127094-2018-0018, arXiv:1603.09684.
Christian Borgs, Jennifer T. Chayes, Henry Cohn, and Yufei Zhao, An Lp theory of sparse graph convergence II: LD convergence, quotients and right convergence, Ann. Probab. 46 (2018), no. 1, 337–396, doi:10.1214/17-AOP1187, arXiv:1408.0744.
2017
Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska, The sphere packing problem in dimension 24, Ann. of Math. (2) 185 (2017), no. 3, 1017–1033, doi:10.4007/annals.2017.185.3.8, arXiv:1603.06518.
Jonah Blasiak, 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, doi:10.19086/da.1245, arXiv:1605.06702.
Henry Cohn, A conceptual breakthrough in sphere packing, Notices Amer. Math. Soc. 64 (2017), no. 2, 102–115, doi:10.1090/noti1474, arXiv:1611.01685.
Christian Borgs, 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, arXiv:1601.07134.
Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, and Chris Umans, Which groups are amenable to proving exponent two for matrix multiplication?, preprint, 2017, arXiv:1712.02302.
Henry Cohn, Packing, coding, and ground states, Mathematics and materials, IAS/Park City Math. Ser., no. 23, Amer. Math. Soc., Providence, RI, 2017, pp. 45–102, arXiv:1603.05202.
2016
Henry Cohn, Abhinav Kumar, and Gregory Minton, Optimal simplices and codes in projective spaces, Geom. Topol. 20 (2016), no. 3, 1289–1357, doi:10.2140/gt.2016.20.1289, arXiv:1308.3188.
Henry Cohn and Stephen D. Miller, Some properties of optimal functions for sphere packing in dimensions 8 and 24, preprint, 2016, arXiv:1603.04759.
2015
Henry Cohn and Nadia Heninger, Ideal forms of Coppersmith’s theorem and Guruswami-Sudan list decoding, Adv. Math. Commun. 9 (2015), no. 3, 311–339, doi:10.3934/amc.2015.9.311, arXiv:1008.1284.
Henry Cohn and Abhinav Kumar, Metacommutation of Hurwitz primes, Proc. Amer. Math. Soc. 143 (2015), no. 4, 1459–1469, doi:10.1090/S0002-9939-2014-12358-6, arXiv:1307.0443.
2014
Henry Cohn and Yufei Zhao, Sphere packing bounds via spherical codes, Duke Math. J. 163 (2014), no. 10, 1965–2002, doi:10.1215/00127094-2738857, arXiv:1212.5966.
Henry Cohn and Yufei Zhao, Energy-minimizing error-correcting codes, IEEE Trans. Inform. Theory 60 (2014), no. 12, 7442–7450, doi:10.1109/TIT.2014.2359201, arXiv:1212.1913.
Nir Bitansky, 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, Advances in Cryptology—CRYPTO 2014, Lecture Notes in Comput. Sci., no. 8617, Springer, Heidelberg, 2014, pp. 71–89, doi:10.1007/978-3-662-44381-1_5, arXiv:1401.0348.
Henry Cohn, Abhinav Kumar, Christian Reiher, and Achill Schürmann, Formal duality and generalizations of the Poisson summation formula, Discrete geometry and algebraic combinatorics, Contemp. Math., no. 625, Amer. Math. Soc., Providence, RI, 2014, pp. 123–140, doi:10.1090/conm/625/12495, arXiv:1306.6796.
2013
Henry Cohn and Nadia Heninger, Approximate common divisors via lattices, ANTS X—Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Ser., no. 1, Math. Sci. Publ., Berkeley, CA, 2013, pp. 271–293, doi:10.2140/obs.2013.1.271, arXiv:1108.2714.
Henry Cohn and Christopher Umans, Fast matrix multiplication using coherent configurations, Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, PA, 2013, pp. 1074–1087, doi:10.1137/1.9781611973105.77, arXiv:1207.6528.
2012
Henry Cohn and Jeechul Woo, Three-point bounds for energy minimization, J. Amer. Math. Soc. 25 (2012), no. 4, 929–958, doi:10.1090/S0894-0347-2012-00737-1, arXiv:1103.0485.
Douglas N. Arnold and Henry Cohn, Mathematicians take a stand, Notices Amer. Math. Soc. 59 (2012), no. 6, 828–833, doi:10.1090/noti857, arXiv:1204.1351.
2011
Henry Cohn, Yang Jiao, Abhinav Kumar, and Salvatore Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), no. 4, 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060.
2010
Henry Cohn, Order and disorder in energy minimization, Proceedings of the International Congress of Mathematicians, Hyderabad, August 19–27, 2010, Volume IV, Hindustan Book Agency, New Delhi, 2010, pp. 2416–2443, arXiv:1003.3053.
Henry Cohn, Noam D. Elkies, Abhinav Kumar, and Achill Schürmann, Point configurations that are asymmetric yet balanced, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2863–2872, doi:10.1090/S0002-9939-10-10284-6, arXiv:0812.2579.
2009
Henry Cohn and Abhinav Kumar, Optimality and uniqueness of the Leech lattice among lattices, Ann. of Math. (2) 170 (2009), no. 3, 1003–1050, doi:10.4007/annals.2009.170.1003, arXiv:math.MG/0403263.
Henry Cohn and Abhinav Kumar, Algorithmic design of self-assembling structures, Proc. Natl. Acad. Sci. USA 106 (2009), no. 24, 9570–9575, doi:10.1073/pnas.0901636106, arXiv:0906.3550.
Henry Cohn, Abhinav Kumar, and Achill Schürmann, Ground states and formal duality relations in the Gaussian core model, Phys. Rev. E (3) 80 (2009), no. 6, 061116, doi:10.1103/PhysRevE.80.061116, arXiv:0911.2169.
Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, and Achill Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), no. 3, 257–283, arXiv:math/0611451, https://projecteuclid.org/euclid.em/1259158465.
2008
Henry Cohn and Abhinav Kumar, Counterintuitive ground states in soft-core models, Phys. Rev. E (3) 78 (2008), no. 6, 061113, doi:10.1103/PhysRevE.78.061113, arXiv:0811.1236.
2007
Henry Cohn and Abhinav Kumar, Universally optimal distribution of points on spheres, J. Amer. Math. Soc. 20 (2007), no. 1, 99–148, doi:10.1090/S0894-0347-06-00546-7, arXiv:math.MG/0607446.
Henry Cohn, John H. Conway, Noam D. Elkies, and Abhinav Kumar, The D4 root system is not universally optimal, Experiment. Math. 16 (2007), no. 3, 313–320, arXiv:math.MG/0607447, https://projecteuclid.org/euclid.em/1204928532.
Henry Cohn and Abhinav Kumar, Uniqueness of the (22,891,1/4) spherical code, New York J. Math. 13 (2007), 147–157, arXiv:math.MG/0607448, https://nyjm.albany.edu/j/2007/13_147.html.
2006
Henry Cohn, A short proof of the simple continued fraction expansion of e, Amer. Math. Monthly 113 (2006), no. 1, 57–62, doi:10.2307/27641837, arXiv:math.NT/0601660.
2005
Henry Cohn, Robert Kleinberg, Balázs Szegedy, and Christopher Umans, Group-theoretic algorithms for matrix multiplication, Proceedings of the 46th Annual Symposium on Foundations of Computer Science, IEEE Computer Society, 2005, pp. 379–388, doi:10.1109/SFCS.2005.39, arXiv:math.GR/0511460.
2004
Henry Cohn and Abhinav Kumar, The densest lattice in twenty-four dimensions, Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 58–67, doi:10.1090/S1079-6762-04-00130-1, arXiv:math.MG/0408174.
Henry Cohn, Projective geometry over F1 and the Gaussian binomial coefficients, Amer. Math. Monthly 111 (2004), no. 6, 487–495, doi:10.2307/4145067, arXiv:math.CO/0407093.
2003
Henry Cohn and Noam Elkies, New upper bounds on sphere packings I, Ann. of Math. (2) 157 (2003), no. 2, 689–714, doi:10.4007/annals.2003.157.689, arXiv:math.MG/0110009.
Henry Cohn and Christopher Umans, A group-theoretic approach to fast matrix multiplication, Proceedings of the 44th Annual Symposium on Foundations of Computer Science, IEEE Computer Society, 2003, pp. 438–449, doi:10.1109/SFCS.2003.1238217, arXiv:math.GR/0307321.
2002
Henry Cohn, New upper bounds on sphere packings II, Geom. Topol. 6 (2002), 329–353, doi:10.2140/gt.2002.6.329, arXiv:math.MG/0110010.
Henry Cohn, Robin Pemantle, and James Propp, Generating a random sink-free orientation in quadratic time, Electron. J. Combin. 9 (2002), no. 1, Research Paper 10, 13 pages, doi:10.37236/1627, arXiv:math.PR/0103189.
2001
Henry Cohn, Richard Kenyon, and James Propp, A variational principle for domino tilings, J. Amer. Math. Soc. 14 (2001), no. 2, 297–346, doi:10.1090/S0894-0347-00-00355-6, arXiv:math.CO/0008220.
1999
Henry Cohn, 2-adic behavior of numbers of domino tilings, Electron. J. Combin. 6 (1999), Research Paper 14, 7 pages, doi:10.37236/1446, arXiv:math.CO/0008222.
1998
Henry Cohn, Michael Larsen, and James Propp, The shape of a typical boxed plane partition, New York J. Math. 4 (1998), 137–165, arXiv:math.CO/9801059, https://nyjm.albany.edu/j/1998/4_137.html.
1996
Henry Cohn, Noam Elkies, and James Propp, Local statistics for random domino tilings of the Aztec diamond, Duke Math. J. 85 (1996), no. 1, 117–166, doi:10.1215/S0012-7094-96-08506-3, arXiv:math.CO/0008243.
Henry Cohn, Symmetry and specializability in continued fractions, Acta Arith. 75 (1996), no. 4, 297–320, doi:10.4064/aa-75-4-297-320, arXiv:math.NT/0008221.