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Henry Cohn

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Henry Cohn
Henry Cohn at Oberwolfach, June 2014
Photo by Ivonne Vetter
Alma materMIT[2]
Harvard
Known forSphere packing
Scientific career
FieldsMathematics
InstitutionsMicrosoft Research
Thesis New Bounds on Sphere Packings  (2000)
Doctoral advisorNoam Elkies[1]
Websitehttps://cohn.mit.edu/

Henry Cohn is an American mathematician. He is a principal researcher at Microsoft Research and an adjunct professor at MIT.[2] Cohn graduated from Harvard University in 2000 with a doctorate in mathematics.[3] Cohn was an Erdős Lecturer at Hebrew University of Jerusalem in 2008. In 2016, he became a Fellow of the American Mathematical Society "for contributions to discrete mathematics, including applications to computer science and physics."[4]

In 2018, he was awarded the Levi L. Conant Prize for his article “A Conceptual Breakthrough in Sphere Packing,” published in 2017[5] in the Notices of the AMS.[6]

Research

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In 2003, with Chris Umans, Cohn initiated a group-theoretic approach to matrix multiplication,[7] and is a core contributor to its continued development with various coauthors.[8][9][10][11][12]

In 2004, Cohn and Noam Elkies used linear programming methods to prove[13] upper bounds on sphere packings in all dimensions. Their conjecture 8.1 suggested "magic" optimizing functions existed in dimensions 2, 8, and 24.

In March 2016 Maryna Viazovska published[14] an arXiv preprint with such a magic function - a weakly holomorphic quasimodular form - proving the optimality of the E8 lattice packing. Cohn contacted Viazovska, and within a week, Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Viazovska had similarly solved the sphere packing problem in 24 dimensions via the Leech lattice Λ24.[15] [16]

References

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  1. ^ Henry Cohn at the Mathematics Genealogy Project
  2. ^ a b "Henry Cohn". Retrieved 14 July 2017.
  3. ^ "Henry Cohn | MIT Mathematics". Archived from the original on 2022-02-19. Retrieved 2017-12-22.
  4. ^ List of Fellows of the American Mathematical Society, retrieved 2017-08-09
  5. ^ Cohn, Henry (February 2017). "A Conceptual Breakthrough in Sphere Packing". Notices of the American Mathematical Society. 64 (02): 102–115. doi:10.1090/noti1474. ISSN 0002-9920.
  6. ^ "2018 Levi L. Conant Prize" (PDF). American Mathematical Society. Retrieved 7 September 2018.
  7. ^ Cohn, Henry; Umans, Christopher (2003). "A group-theoretic approach to fast matrix multiplication". Proc. 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE. pp. 438–449. arXiv:math/0307321. doi:10.1109/SFCS.2003.1238217.
  8. ^ Cohn, Henry; Kleinberg, Robert; Szegedy, Balász; Umans, Christopher (2005). "Group-theoretic Algorithms for Matrix Multiplication". Proc. 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE. pp. 379–388. arXiv:math/0511460. doi:10.1109/SFCS.2005.39.
  9. ^ Cohn, Henry; Umans, Christopher (2013). "Fast matrix multiplication using coherent configurations". Proc. 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SIAM. pp. 1074–1087. arXiv:1207.6528. doi:10.1137/1.9781611973105.77.
  10. ^ Blasiak, Jonah; Church, Thomas; Cohn, Henry; Grochow, Joshua A.; Naslund, Eric; Sawin, William F.; Umans, Christopher (2017). "On cap sets and the group-theoretic approach to matrix multiplication". Discrete Analysis. arXiv:1605.06702. doi:10.19086/da.1245.
  11. ^ Blasiak, Jonah; Church, Thomas; Cohn, Henry; Grochow, Joshua A.; Umans, Christopher (2017). "Which groups are amenable to proving exponent two for matrix multiplication?". arXiv:1712.02302 [math.GR].
  12. ^ Blasiak, Jonah; Cohn, Henry; Grochow, Joshua A.; Pratt, Kevin; Umans, Christopher (2023). "Matrix Multiplication via Matrix Groups". 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. pp. 19:1–19:16. doi:10.4230/LIPIcs.ITCS.2023.19.
  13. ^ Cohn, Henry; Elkies, Noam (1 March 2003). "New upper bounds on sphere packings I" (PDF). Annals of Mathematics. 157 (2): 689–714. doi:10.4007/annals.2003.157.689. ISSN 0003-486X. Retrieved 19 January 2025.
  14. ^ Viazovska, Maryna (1 May 2017). "The sphere packing problem in dimension $8$". Annals of Mathematics. 185 (3). Annals of Mathematics: 991–1015. doi:10.4007/annals.2017.185.3.7. ISSN 0003-486X. Retrieved 19 January 2025.
  15. ^ Klarreich, Erica (30 March 2016). "Sphere Packing Solved in Higher Dimensions". Quanta Magazine. Retrieved 14 July 2017.
  16. ^ Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 May 2017). "The sphere packing problem in dimension $24$". Annals of Mathematics. 185 (3): 1017–1033. doi:10.4007/annals.2017.185.3.8. ISSN 0003-486X. Retrieved 19 January 2025.
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