Henry Cohn

Henry Cohn
Henry Cohn at Oberwolfach, June 2014
Photo by Ivonne Vetter
Alma materHarvard University
Known forSphere packing
Scientific career
FieldsMathematics
Workplaces
Thesis New Bounds on Sphere Packings  (2000)
Noam Elkies[1]
Websitehttps://cohn.mit.edu/

Henry Cohn is an American mathematician. He is currently a 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

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

  1. ^ Henry Cohn at the Mathematics Genealogy Project
  2. ^ "Henry Cohn". Retrieved 5 October 2025.
  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 (2): 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): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. ISSN 0003-486X.
  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. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8. ISSN 0003-486X.
Flag of United StatesScientist icon

This article about an American mathematician is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.