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Andreas Floer

January 06, 2023

Andreas Floer (German: [ˈfløːɐ]; 23 August 1956 – 15 May 1991) was a German mathematician who made seminal contributions to symplectic topology, and mathematical physics, in particular the invention of Floer homology. Floer's first pivotal contribution was a solution of a special case of Arnold's conjecture on fixed points of a symplectomorphism. Because of his work on Arnold's conjecture and his development of instanton homology, he achieved wide recognition and was invited as a plenary speaker for the International Congress of Mathematicians held in Kyoto in August 1990. He received a Sloan Fellowship in 1989.

Andreas Floer
Andreas Floer in 1975
Born(1956-08-23)August 23, 1956
Duisburg, West Germany
DiedMay 15, 1991(1991-05-15) (aged 34)
NationalityGerman
Alma materRuhr-Universität Bochum
Known forFloer homology
Scientific career
FieldsMathematics
InstitutionsRuhr-Universität Bochum
University of California, Berkeley
Doctoral advisorEduard Zehnder
Ralf Stöcker

Life

He was an undergraduate student at the Ruhr-Universität Bochum and received a Diplom in mathematics in 1982. He then went to the University of California, Berkeley, living at Barrington Hall of the Berkeley Student Cooperative, and undertook Ph.D. work on monopoles on 3-manifolds, under the supervision of Clifford Taubes; but he did not complete it when interrupted by his obligatory alternative service in Germany.[1] He received his Dr. rer. nat. at Bochum in 1984, under the supervision of Eduard Zehnder.

In 1988 he became an Assistant Professor at the University of California, Berkeley and was promoted to Full Professor of Mathematics in 1990. From 1990 he was Professor of Mathematics at the Ruhr-Universität Bochum, until his suicide in 1991 as a result of depression.[2]

Quotes

"Andreas Floer's life was tragically interrupted, but his mathematical visions and striking contributions have provided powerful methods which are being applied to problems which seemed to be intractable only a few years ago."[1]

Simon Donaldson wrote: "The concept of Floer homology is one of the most striking developments in differential geometry over the past 20 years. ... The ideas have led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory"[2] and "the full richness of Floer's theory is only beginning to be explored".[3]

"Since its introduction by Andreas Floer in the late nineteen eighties, Floer theory has had a tremendous influence on many branches of mathematics including geometry, topology and dynamical systems. The development of new Floer theoretic tools continues at a remarkable pace and underlies many of the recent breakthroughs in these diverse fields."[4]

Selected publications

  • Floer, Andreas. An instanton-invariant for 3-manifolds. Comm. Math. Phys. 118 (1988), no. 2, 215–240. Project Euclid
  • Floer, Andreas. Morse theory for Lagrangian intersections. J. Differential Geom. 28 (1988), no. 3, 513–547.
  • Floer, Andreas. Cuplength estimates on Lagrangian intersections. Comm. Pure Appl. Math. 42 (1989), no. 4, 335–356.

Posthumous publications

  • Hofer, Helmut. Coherent orientation for periodic orbit problems in symplectic geometry (jointly with A. Floer) Math. Zeit. 212, 13–38, 1993.
  • Hofer, Helmut. Symplectic homology I: Open sets in C^n (jointly with A. Floer) Math. Zeit. 215, 37–88, 1994.
  • Hofer, Helmut. Applications of symplectic homology I (jointly with A. Floer and K. Wysocki) Math. Zeit. 217, 577–606, 1994.
  • Hofer, Helmut. Symplectic homology II: A General Construction (jointly with K. Cieliebak and A. Floer) Math. Zeit. 218, 103–122, 1995.
  • Hofer, Helmut. Transversality results in the elliptic Morse theory of the action functional (jointly with A. Floer and D. Salamon) Duke Mathematical Journal, Vol. 80 No. 1, 251–292, 1995. Download from H. Hofer's homepage at NYU
  • Hofer, Helmut. Applications of symplectic homology II (jointly with K. Cieliebak, A. Floer and K. Wysocki) Math. Zeit. 223, 27–45, 1996.

Notes

  1. ^ Hofer, Weinstein, and Zehnder, Andreas Floer: 1956-1991, Notices Amer. Math. Soc. 38 (8), 910-911
  2. ^ Simon Donaldson, Floer Homology Groups in Yang-Mills Theory, With the assistance of M. Furuta and D. Kotschick. Cambridge Tracts in Mathematics, 147. Cambridge University Press, Cambridge, 2002. viii+236 pp. ISBN 0-521-80803-0 (The above citation is from the front flap.)
  3. ^ Mathematics: frontiers and perspectives. Edited by V. Arnold, M. Atiyah, P. Lax and B. Mazur. American Mathematical Society, Providence, RI, 2000. xii+459 pp. ISBN 0-8218-2070-2 (Amazon search)
  4. ^ From the Press Release to the Workshop New Applications and Generalizations of Floer Theory of the Banff International Research Station (BIRS), May 2007 ([5])

Further reading

  • Simon Donaldson, On the work of Andreas Floer, Jahresber. Deutsch. Math.-Verein. 95 (3) (1993), 103-120.
  • The Floer Memorial Volume (H. Hofer, C. Taubes, A. Weinstein, and E. Zehnder, eds.), Progress in Mathematics, vol. 133, Birkhauser Verlag, 1995.
  • Simon Donaldson, Floer Homology Groups in Yang-Mills Theory, With the assistance of M. Furuta and D. Kotschick. Cambridge Tracts in Mathematics, 147. Cambridge University Press, Cambridge, 2002. viii+236 pp. ISBN 0-521-80803-0

References

  1. ^ Harris, Michael (2015). Mathematics Without Apologies: Portrait of a Problematic Vocation. Princeton University Press. pp. 216–217. ISBN 978-0-691-15423-7.
  2. ^ Berg, Michael (2 February 2014). "MAA Book Review: Morse Theory and Floer Homology". Retrieved 11 December 2021.

External links

  • O'Connor, John J.; Robertson, Edmund F., "Andreas Floer", MacTutor History of Mathematics archive, University of St Andrews
  • Andreas Floer at the Mathematics Genealogy Project
  • The In Memoriam website of the Department of Mathematics at the University of California, Berkeley
  • Elaborate obituary by Addison/Casson/Weinstein at OAC, Online Archive of California, 1992
  • For images, see Wikimedia Commons Category:Andreas Floer and a public Andreas Floer photo album on Facebook
  • Video of Andreas Floer giving a lecture on the Arnold Conjecture, Stony Brook 1986 (access forbidden; 2021-Jul-16). YouTube alternative
  • Introduction to Floer Theory. Lecture by Dusa McDuff 2010
  • Introduction to Floer Theory? at mathoverflow.net

January 06, 2023
andreas, floer, german, ˈfløːɐ, august, 1956, 1991, german, mathematician, made, seminal, contributions, symplectic, topology, mathematical, physics, particular, invention, floer, homology, floer, first, pivotal, contribution, solution, special, case, arnold, . Andreas Floer German ˈfloːɐ 23 August 1956 15 May 1991 was a German mathematician who made seminal contributions to symplectic topology and mathematical physics in particular the invention of Floer homology Floer s first pivotal contribution was a solution of a special case of Arnold s conjecture on fixed points of a symplectomorphism Because of his work on Arnold s conjecture and his development of instanton homology he achieved wide recognition and was invited as a plenary speaker for the International Congress of Mathematicians held in Kyoto in August 1990 He received a Sloan Fellowship in 1989 Andreas FloerAndreas Floer in 1975Born 1956 08 23 August 23 1956Duisburg West GermanyDiedMay 15 1991 1991 05 15 aged 34 NationalityGermanAlma materRuhr Universitat BochumKnown forFloer homologyScientific careerFieldsMathematicsInstitutionsRuhr Universitat BochumUniversity of California BerkeleyDoctoral advisorEduard ZehnderRalf Stocker Contents 1 Life 2 Quotes 3 Selected publications 4 Posthumous publications 5 Notes 6 Further reading 7 References 8 External linksLife EditHe was an undergraduate student at the Ruhr Universitat Bochum and received a Diplom in mathematics in 1982 He then went to the University of California Berkeley living at Barrington Hall of the Berkeley Student Cooperative and undertook Ph D work on monopoles on 3 manifolds under the supervision of Clifford Taubes but he did not complete it when interrupted by his obligatory alternative service in Germany 1 He received his Dr rer nat at Bochum in 1984 under the supervision of Eduard Zehnder In 1988 he became an Assistant Professor at the University of California Berkeley and was promoted to Full Professor of Mathematics in 1990 From 1990 he was Professor of Mathematics at the Ruhr Universitat Bochum until his suicide in 1991 as a result of depression 2 Quotes Edit Andreas Floer s life was tragically interrupted but his mathematical visions and striking contributions have provided powerful methods which are being applied to problems which seemed to be intractable only a few years ago 1 Simon Donaldson wrote The concept of Floer homology is one of the most striking developments in differential geometry over the past 20 years The ideas have led to great advances in the areas of low dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory 2 and the full richness of Floer s theory is only beginning to be explored 3 Since its introduction by Andreas Floer in the late nineteen eighties Floer theory has had a tremendous influence on many branches of mathematics including geometry topology and dynamical systems The development of new Floer theoretic tools continues at a remarkable pace and underlies many of the recent breakthroughs in these diverse fields 4 Selected publications EditFloer Andreas An instanton invariant for 3 manifolds Comm Math Phys 118 1988 no 2 215 240 Project Euclid Floer Andreas Morse theory for Lagrangian intersections J Differential Geom 28 1988 no 3 513 547 Floer Andreas Cuplength estimates on Lagrangian intersections Comm Pure Appl Math 42 1989 no 4 335 356 Posthumous publications EditHofer Helmut Coherent orientation for periodic orbit problems in symplectic geometry jointly with A Floer Math Zeit 212 13 38 1993 Hofer Helmut Symplectic homology I Open sets in C n jointly with A Floer Math Zeit 215 37 88 1994 Hofer Helmut Applications of symplectic homology I jointly with A Floer and K Wysocki Math Zeit 217 577 606 1994 Hofer Helmut Symplectic homology II A General Construction jointly with K Cieliebak and A Floer Math Zeit 218 103 122 1995 Hofer Helmut Transversality results in the elliptic Morse theory of the action functional jointly with A Floer and D Salamon Duke Mathematical Journal Vol 80 No 1 251 292 1995 Download from H Hofer s homepage at NYU Hofer Helmut Applications of symplectic homology II jointly with K Cieliebak A Floer and K Wysocki Math Zeit 223 27 45 1996 Notes Edit Hofer Weinstein and Zehnder Andreas Floer 1956 1991 Notices Amer Math Soc 38 8 910 911 Simon Donaldson Floer Homology Groups in Yang Mills Theory With the assistance of M Furuta and D Kotschick Cambridge Tracts in Mathematics 147 Cambridge University Press Cambridge 2002 viii 236 pp ISBN 0 521 80803 0 The above citation is from the front flap Mathematics frontiers and perspectives Edited by V Arnold M Atiyah P Lax and B Mazur American Mathematical Society Providence RI 2000 xii 459 pp ISBN 0 8218 2070 2 Amazon search From the Press Release to the Workshop New Applications and Generalizations of Floer Theory of the Banff International Research Station BIRS May 2007 5 Further reading EditSimon Donaldson On the work of Andreas Floer Jahresber Deutsch Math Verein 95 3 1993 103 120 The Floer Memorial Volume H Hofer C Taubes A Weinstein and E Zehnder eds Progress in Mathematics vol 133 Birkhauser Verlag 1995 Simon Donaldson Floer Homology Groups in Yang Mills Theory With the assistance of M Furuta and D Kotschick Cambridge Tracts in Mathematics 147 Cambridge University Press Cambridge 2002 viii 236 pp ISBN 0 521 80803 0References Edit Harris Michael 2015 Mathematics Without Apologies Portrait of a Problematic Vocation Princeton University Press pp 216 217 ISBN 978 0 691 15423 7 Berg Michael 2 February 2014 MAA Book Review Morse Theory and Floer Homology Retrieved 11 December 2021 External links EditO Connor John J Robertson Edmund F Andreas Floer MacTutor History of Mathematics archive University of St Andrews Andreas Floer at the Mathematics Genealogy Project The In Memoriam website of the Department of Mathematics at the University of California Berkeley The In Memoriam website of the University of California Berkeley Elaborate obituary by Addison Casson Weinstein at OAC Online Archive of California 1992 For images see Wikimedia Commons Category Andreas Floer and a public Andreas Floer photo album on Facebook Video of Andreas Floer giving a lecture on the Arnold Conjecture Stony Brook 1986 access forbidden 2021 Jul 16 YouTube alternative Introduction to Floer Theory Lecture by Dusa McDuff 2010 Introduction to Floer Theory at mathoverflow net Retrieved from https en wikipedia org w index php title Andreas Floer amp oldid 1130199040, wikipedia, wiki, book, books, library,

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