Michael J. Hopkins

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Michael J. Hopkins, Edinburgh 2009

Michael Jerome Hopkins (born April 18, 1958 in Alexandria (Virginia) ) is an American mathematician who deals with algebraic topology , especially homotopy theory.

Hopkins, who by his own admission initially wanted to be a rock musician, studied mathematics at Northwestern University , where he received his bachelor's degree in 1979 . He then went to Oxford University , where he worked with Ioan James as Dr. Phil. PhD. Another time, he received his doctorate in the same year at Northwestern University when Mark Mahowald as a Ph.D. He was then from 1984 to 1987 as a post-doctoral student and later assistant professor at Princeton University , 1988/89 as professor at the University of Chicago , from 1989 associate professor and from 1990 professor at the Massachusetts Institute of Technology (MIT). Since 2005 he has been a professor at Harvard University .

Hopkins was a Sloan Research Fellow from 1987 . In 1994 he was invited speaker at the International Congress of Mathematicians (ICM) in Zurich with the lecture topic "Topological modular forms, the Witten genus and the theorem of the cube" and gave a plenary lecture on "Algebraic Topology and Modular Forms" at the ICM 2002 in Beijing. . In 2000 he gave the Marston Morse Memorial Lectures at the Institute for Advanced Study .

In 2009, together with his former doctoral students Michael A. Hill and Douglas Ravenel, he achieved an almost complete solution to the Kervaire invariant problem (after Michel Kervaire ). With Haynes Miller he introduced topological modular forms as part of a geometric interpretation of elliptical cohomology .

In 2001 he received the Oswald Veblen Prize for his work on Nilpotenz and periodicity in stable homotopy theory (proof of a large part of the Ravenel conjectures with Ethan Devinatz , Jeffrey H. Smith ), for his work on "rigid analytic geometry" and its application in homotopy theory and for his work on elliptical spectra (partly with Matthew Ando, Neil Strickland ). In 2002 he was elected to the American Academy of Arts and Sciences , and in 2010 to the National Academy of Sciences . In 2012 he received the NAS Award in Mathematics and in 2014 both the Nemmers Prize in Mathematics from Northwestern University and the Senior Berwick Prize . In November 2019 he gave a Gauss lecture .

Web links

Fonts (selection)

  • Nilpotence and stable homotopy theory. I (with E. Devinatz, J. Smith): Ann. of Math. (2) 128 (1988) no. 2, 207-241. II (with J. Smith): Ann. of Math. (2) 148 (1998) no. 1, 1-49.
  • with N. Kuhn, D. Ravenel: Generalized group characters and complex oriented cohomology theories. J. Amer. Math. Soc. 13 (2000), no. 3, 553-594
  • with M. Ando, ​​N. Strickland: Elliptic spectra, the Witten genus and the theorem of the cube. Invent. Math. 146 (2001), no. 3, 595-687.
  • with E. Devinatz: Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups. Topology 43 (2004), no. 1, 1-47.
  • with P. Goerss : Moduli spaces of commutative ring spectra. Structured ring spectra, 151-200, London Math. Soc. Lecture Note Ser., 315, Cambridge Univ. Press, Cambridge, 2004.
  • with I. Singer : Quadratic functions in geometry, topology, and M-theory. J. Differential Geom. 70 (2005) no. 3, 329-452.
  • with D. Freed , C. Teleman : Loop groups and twisted K-theory III. Ann. of Math. (2) 174 (2011), no. 2, 947-1007.
  • with MA Hill, DC Ravenel: On the nonexistence of elements of Kervaire invariant one . In: Annals of Mathematics . tape 184 , no. 1 , July 2016, p. 1-262 . , Arxiv

References and comments

  1. ↑ Portrait at Harvard University 2006 ( Memento of the original from July 12, 2009 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.news.harvard.edu
  2. ↑ Michael J. Hopkins in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  3. ^ Haynes Miller : Kervaire invariant one [after MA Hill, MJ Hopkins, and DC Ravenel] . In: Séminaire Bourbaki . 63rd year. No. 1029 , November 2010, see pp. 1029–02 ( online [PDF; accessed January 18, 2016]).
  4. ↑ Ethan Devinatz, Jeff Smith, Hopkins: Nilpotence and stable homotopy theory I, II. Annals of Mathematics Vol. 128, 1988, p. 207, Vol. 148, 1998, pp. 1-49
  5. ^ Dick Gross, Hopkins: Equivariant vector bundles on the Lubin-Tate moduli space. Contemporary Mathematics, Vol. 158, 1994, pp. 23-88; The rigid analytic period mapping, Lubin-Tate space and stable homotopy theory. Bulletin AMS, Vol. 30, 1994, p. 75
personal data
SURNAME Hopkins, Michael J.
ALTERNATIVE NAMES Hopkins, Michael Jerome (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH April 18, 1958
PLACE OF BIRTH Alexandria (Virginia)