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Michael Howard Harris (born 1954) is an American mathematician known for his work in number theory. He is a professor of mathematics at Columbia University and professor emeritus of mathematics at Université Paris Cité.

Early life and education

Harris was born in Kingsessing, Philadelphia, Pennsylvania[1] and is of Jewish descent.[2] He received his B.A. in mathematics from Princeton University in 1973.[3] He received his M.A. and Ph.D. in mathematics from Harvard University under the supervision of Barry Mazur in 1976 and 1977 respectively.[3][4]

Career

Harris was a faculty member at Brandeis University from 1977 to 1994.[3] In 1994, he became a professor of mathematics at Paris Diderot University and the Institut de mathématiques de Jussieu – Paris Rive Gauche, where he has been emeritus since 2021.[3][5] He became a professor of mathematics at Columbia University in 2013.[3]

He was a member of the Institute for Advanced Study from 1983 to 1984 and in the fall of 2011.[6] He has held visiting positions at various institutions, including Bethlehem University, the Steklov Institute of Mathematics, the Institut des Hautes Études Scientifiques, Oxford University, and the Mathematical Sciences Research Institute.[3]

His former doctoral students include Laurent Fargues and Gaëtan Chenevier.[4]

Work

Research

Harris's research focuses on arithmetic geometry, automorphic forms, L-functions, and motives.[7] He has developed the theory of coherent cohomology of Shimura varieties and applied it to number theoretic problems on special values of L-functions, Galois representations, and the theta correspondence.[1] His later work focuses on geometric aspects of the Langlands program.[1]

In 2001, Harris and Richard Taylor proved the local Langlands conjecture for GL(n) over a p-adic local field [8] The Sato–Tate conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008,[9][10][11] and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011.[12]

Mathematics without Apologies

Harris wrote the book Mathematics without Apologies: Portrait of a Problematic Vocation, published in 2015.[13][14][15][16]

Silicon Reckoner

Since 2021, Harris has written the newsletter Silicon Reckoner exploring questions and issues related to the mechanization of mathematics and artificial intelligence.[17]

Recognition

Harris received the Sophie Germain Prize (2006),[3] the Clay Research Award (joint with Richard Taylor, 2007),[1][18] the Grand Prix Scientifique de la Fondation Simone et Cino del Duca (2009),[3] He is a three-time invited speaker at the International Congress of Mathematicians (2000, 2002, 2014).[3]

He was a Sloan Research Fellow (1983–1985) and a member of the Institut Universitaire de France (2001–2011)[3][1] He has been elected a Member of the Academia Europaea (2016),[3] Fellow of the American Mathematical Society (2019),[3][7] Member of the American Academy of Arts and Sciences (2019),[3] and Member of the National Academy of Sciences (2022).[1][3]

References

  1. ^ a b c d e f "Michael Harris". National Academy of Sciences. National Academy of Sciences. Retrieved June 24, 2023.
  2. ^ Harris, Michael (2015). Mathematics without Apologies: Portrait of a Problematic Vocation. Princeton University Press. p. 373. ISBN 9780691154237.
  3. ^ a b c d e f g h i j k l m n Harris, Michael. "CV". Michael Harris. Retrieved July 24, 2023.
  4. ^ a b Michael Harris at the Mathematics Genealogy Project
  5. ^ "Emérites". Institut de mathématiques de Jussieu – Paris Rive Gauche. Institut de mathématiques de Jussieu – Paris Rive Gauche. Retrieved June 24, 2023.
  6. ^ "Michael Harris". Institute for Advanced Study. Institute for Advanced Study. Retrieved June 24, 2023.
  7. ^ a b "2019 Class of the Fellows of the AMS". American Mathematical Society. American Mathematical Society. Retrieved June 24, 2023.
  8. ^ Harris, Michael; Taylor, Richard (2001), The geometry and cohomology of some simple Shimura varieties, ISBN 978-0-691-09092-4, MR 1876802
  9. ^ Taylor, Richard (2008). "Automorphy for some l-adic lifts of automorphic mod l Galois representations. II". Publ. Math. Inst. Hautes Études Sci. 108: 183–239. CiteSeerX 10.1.1.116.9791. doi:10.1007/s10240-008-0015-2. MR 2470688.
  10. ^ Clozel, Laurent; Harris, Michael; Taylor, Richard (2008). "Automorphy for some l-adic lifts of automorphic mod l Galois representations". Publ. Math. Inst. Hautes Études Sci. 108: 1–181. CiteSeerX 10.1.1.143.9755. doi:10.1007/s10240-008-0016-1. MR 2470687.
  11. ^ Harris, Michael; Shepherd-Barron, Nicholas; Taylor, Richard (2010), "A family of Calabi–Yau varieties and potential automorphy", Annals of Mathematics, 171 (2): 779–813, doi:10.4007/annals.2010.171.779, MR 2630056
  12. ^ Barnet-Lamb, Thomas; Geraghty, David; Harris, Michael; Taylor, Richard (2011). "A family of Calabi–Yau varieties and potential automorphy. II". Publ. Res. Inst. Math. Sci. 47 (1): 29–98. doi:10.2977/PRIMS/31. MR 2827723.
  13. ^ Harris, Michael (2015). Mathematics without apologies : portrait of a problematic vocation. Princeton University Press. ISBN 978-1-4008-5202-4. OCLC 900080550.
  14. ^ McCleary, John (November 2018). "Review of Mathematics without Apologies: Portrait of a Problematic Vocation by Michael Harris" (PDF). Notices of the AMS.
  15. ^ Alexander, Amir (4 March 2015). "Mathematics: Groping in the dark for glimpses of beauty (joint review of Birth of a Theorem by Cédric Villani and Mathematics without Apologies by Michael Harris)". Nature. 519 (7541): 31–32. doi:10.1038/519031a. (See Cédric Villani.)
  16. ^ Hunacek, Michael (August 4, 2015). "review of Mathematics without Apologies". MAA Reviews.
  17. ^ Harris, Michael. "About Silicon Reckoner".
  18. ^ "Clay Award". Archived from the original on 2012-03-16. Retrieved 2011-06-01.

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