44:
533:. He was named to the 2021 class of fellows of the American Mathematical Society "for contributions to algebraic topology and related areas of algebraic geometry, representation theory, and mathematical physics". In 2022 he received for the second time the
327:(published in 1988). The rest of the Ravenel conjectures (except for the telescope conjecture) were proven by Hopkins and Smith soon after (published in 1998). Another result in this spirit proven by Hopkins and
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in
Beijing. He presented the 1994 Everett Pitcher Lectures at Lehigh University, the 2000 Namboodiri Lectures at the University of Chicago, the 2000 Marston Morse Memorial Lectures at the
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417:. Subsequent work of Hopkins on this topic includes papers on the question of the orientability of TMF with respect to string cobordism (joint work with Ando, Strickland and Rezk).
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into a problem in stable homotopy theory. The proof by Hill, Hopkins and
Ravenel works purely in the stable homotopy setting and uses equivariant homotopy theory in a crucial way.
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is the chromatic convergence theorem, which states that one can recover a finite CW-complex from its localizations with respect to wedges of
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382:-ring spectra – this allowed to take homotopy fixed points of finite subgroups of the Morava stabilizer groups, which led to higher real
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This part of work is about refining a homotopy commutative diagram of ring spectra up to homotopy to a strictly commutative diagram of
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Ando, Matthew; Hopkins, Michael J.; Strickland, Neil P. (2001), "Elliptic spectra, the Witten genus and the theorem of the cube",
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Hill, Michael A; Hopkins, Michael J; Ravenel, Douglas C (2009), "On the non-existence of elements of
Kervaire invariant one",
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Freed, Daniel S.; Hopkins, Michael J.; Teleman, Constantin (2003), "Twisted K-theory and loop group representations",
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285:. It can roughly be divided into four parts (while the list of topics below is by no means exhaustive):
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is null-homotopic iff it is zero in complex cobordism. This was proven by Ethan
Devinatz, Hopkins and
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386:. Together with Paul Goerss, Hopkins later set up a systematic obstruction theory for refinements to
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Multiplicative orientations of KO-theory and of the spectrum of topological modular forms
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Proceedings of the
International Congress of Mathematicians, ZĂĽrich, Switzerland 1994
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stabilizer group on Lubin–Tate spectra (arising out of the deformation theory of
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875:"Topological modular forms, the Witten genus, and the theorem of the cube"
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413:-ring spectra. This was later used in the Hopkins–Miller construction of
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221:(born April 18, 1958) is an American mathematician known for work in
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and the 2010 Bowen
Lectures in Berkeley. In 2001 he was awarded the
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Hopkins, M. J. (2002). "Algebraic topology and modular forms".
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Hopkins' work concentrates on algebraic topology, especially
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He gave invited addresses at the 1990 Winter
Meeting of the
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Members of the United States
National Academy of Sciences
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On April 21, 2009, Hopkins announced the solution of the
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A celebration of the mathematical legacy of Raoul Bott
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361:
245:. Also in 1984 he also received his D.Phil. from the
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Harvard
University Department of Mathematics faculty
620:(1998), "Nilpotence and Stable Homotopy Theory II",
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Hopkins–Miller theorem and topological modular forms
572:(1988), "Nilpotence and Stable Homotopy Theory I",
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493:in Zurich, and was a plenary speaker at the 2002
1283:Massachusetts Institute of Technology faculty
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8:
1303:Fellows of the American Mathematical Society
437:. This problem is connected to the study of
243:Stable Decompositions of Certain Loop Spaces
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319:of some iteration of a map between finite
253:. He has been professor of mathematics at
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31:
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668:Moduli spaces of commutative ring spectra
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568:Devinatz, Ethan S.; Hopkins, Michael J.;
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495:International Congress of Mathematicians
491:International Congress of Mathematicians
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311:than you might think. For example, the
257:since 2005, after fifteen years at the
269:, and a visiting lecturer position at
489:in Louisville, Kentucky, at the 1994
259:Massachusetts Institute of Technology
7:
1258:21st-century American mathematicians
1253:20th-century American mathematicians
994:Oswald Veblen Prize in Geometry 2022
453:This includes papers on smooth and
307:(and its variants) see more in the
1268:Alumni of the University of Oxford
937:Mike Hopkins – Biographical Sketch
686:Goerss – Topological Modular Forms
449:Work connected to geometry/physics
398:
367:
25:
441:, but got transformed by work of
973:2021 Class of Fellows of the AMS
887:. Vol. 1. pp. 554–565.
1045:Oswald Veblen Prize in Geometry
976:, American Mathematical Society
900:Proceedings of the ICM, Beijing
535:Oswald Veblen Prize in Geometry
511:Oswald Veblen Prize in Geometry
461:and also work about (extended)
265:, a one-year position with the
237:in 1984 under the direction of
18:Michael Hopkins (mathematician)
1263:Northwestern University alumni
781:Geometry and Physics: Atiyah80
421:The Kervaire invariant problem
345:highly structured ring spectra
1:
557:Mathematics Genealogy Project
487:American Mathematical Society
261:, a few years of teaching at
1273:Princeton University faculty
531:Nemmers Prize in Mathematics
499:Institute for Advanced Study
406:{\displaystyle E_{\infty }}
375:{\displaystyle A_{\infty }}
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1057:Christos Papakyriakopoulos
463:topological field theories
427:Kervaire invariant problem
292:
103:Kervaire invariant problem
1278:Lehigh University faculty
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415:topological modular forms
249:under the supervision of
233:He received his PhD from
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99:Topological modular forms
41:
705:Inventiones Mathematicae
523:NAS Award in Mathematics
457:and its relationship to
355:) and its refinement to
309:stable homotopy category
120:NAS Award in Mathematics
48:Michael J. Hopkins, 2009
873:Hopkins, M. J. (1994).
837:; Hopkins, Michael J.;
289:The Ravenel conjectures
235:Northwestern University
84:Northwestern University
501:, Princeton, the 2003
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283:stable homotopy theory
219:Michael Jerome Hopkins
29:American mathematician
1209:Fernando Codá Marques
736:10.1007/s002220100175
623:Annals of Mathematics
616:Hopkins, Michael J.;
575:Annals of Mathematics
529:and also in 2014 the
429:, in joint work with
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313:nilpotence conjecture
293:Further information:
267:University of Chicago
527:Senior Berwick Prize
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263:Princeton University
247:University of Oxford
134:Senior Berwick Prize
1137:Richard S. Hamilton
1103:James Harris Simons
922:2002math.....12397H
718:2001InMat.146..595A
507:Columbia University
301:Ravenel conjectures
295:Ravenel conjectures
1155:Michael J. Hopkins
1043:Recipients of the
553:Michael J. Hopkins
475:Constantin Teleman
403:
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303:very roughly say:
255:Harvard University
223:algebraic topology
169:Harvard University
94:Nilpotence theorem
36:Michael J. Hopkins
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1234:
1189:William Minicozzi
1008:2001 Veblen Prize
955:Veblen Prize 2001
618:Smith, Jeffrey H.
570:Smith, Jeffrey H.
353:formal group laws
333:Morava K-theories
315:states that some
305:complex cobordism
271:Lehigh University
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191:Doctoral students
176:Doctoral advisors
151:Scientific career
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16:(Redirected from
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1085:Robion Kirby
1075:Morton Brown
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913:math/0212397
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505:Lectures at
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467:Daniel Freed
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321:CW-complexes
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207:Reid Barton
203:Charles Rezk
165:Institutions
150:
141:Veblen Prize
113:Veblen Prize
26:
1248:1958 births
1213:André Neves
1203:Daniel Wise
1193:Paul Seidel
1161:David Gabai
1079:Barry Mazur
980:November 2,
906:: 283–309.
630:(1): 1–49,
525:, 2014 the
481:Recognition
471:Jacob Lurie
459:loop groups
199:Jacob Lurie
195:Daniel Biss
160:Mathematics
72:Nationality
1242:Categories
1063:Raoul Bott
712:(3): 595,
384:K-theories
325:Jeff Smith
317:suspension
251:Ioan James
185:Ioan James
60:1958-04-18
1141:Gang Tian
852:0905.0731
801:0908.3724
761:CiteSeerX
744:119932563
722:CiteSeerX
632:CiteSeerX
513:from the
431:Mike Hill
399:∞
368:∞
1227:Song Sun
1199:Ian Agol
75:American
918:Bibcode
861:2648901
714:Bibcode
604:0960945
596:1971440
555:at the
859:
763:
742:
724:
654:120991
652:
634:
602:
594:
473:, and
349:Morava
157:Fields
144:(2022)
137:(2014)
130:(2014)
123:(2012)
116:(2001)
109:Awards
1217:2019
1207:2016
1197:2013
1183:2010
1165:2007
1159:2004
1153:and
1145:2001
1135:1996
1125:1991
1119:1986
1113:1981
1107:1981
1101:1976
1095:1976
1089:1971
1083:1971
1073:1966
1067:1966
1061:1964
1055:1964
959:(PDF)
941:(PDF)
908:arXiv
878:(PDF)
847:arXiv
816:arXiv
796:arXiv
740:S2CID
690:(PDF)
672:(PDF)
650:JSTOR
592:JSTOR
541:Notes
1225:and
1211:and
1201:and
1187:and
1177:and
1169:and
1139:and
1129:and
1077:and
982:2020
503:Ritt
433:and
299:The
277:Work
229:Life
54:Born
883:In:
732:doi
710:146
642:doi
628:148
584:doi
580:128
515:AMS
1244::
1221:,
1191:;
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902:.
880:.
857:MR
855:,
759:,
738:,
730:,
720:,
708:,
648:,
640:,
626:,
600:MR
598:,
590:,
578:,
537:.
477:.
469:,
335:.
273:.
225:.
62:)
1036:e
1029:t
1022:v
924:.
920::
910::
904:1
849::
818::
798::
734::
716::
644::
586::
395:E
364:A
58:(
20:)
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