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Andreas Floer at age 19
Andreas Floer at age 19

Andreas Floer [fløːɐ] (August 23, 1956 – May 15, 1991) was a German mathematician who made important, seminal contributions to the areas of geometry, topology, and mathematical physics. Events 79 - Mount Vesuvius begins stirring on the feast day of Vulcan the Roman god of fire Year 1956 ( MCMLVI) was a Leap year starting on Sunday (link will display full calendar of the Gregorian calendar. Events 1252 - Pope Innocent IV issues the Papal bull Ad exstirpanda, which authorizes but also limits the Year 1991 ( MCMXCI) was a Common year starting on Tuesday (link will display full calendar of the Gregorian Calendar. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. A mathematician is a person whose primary area of study and research is the field of Mathematics. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Mathematical physics is the scientific discipline concerned with the interface of Mathematics and Physics. He invented Floer homology, which has proven to be an important tool. Floer homology is a mathematical tool used in the study of Symplectic geometry and low-dimensional Topology.

Contents

Life

He was an undergraduate student at the Ruhr-Universität Bochum and received the degree Diplom-Mathematiker in 1982. Ruhr University Bochum ( German Ruhr-Universität Bochum, RUB) located on the southern hills of central Ruhr area Bochum He then went to the University of California, Berkeley and undertook Ph. The University of California Berkeley (also referred to as Cal, Berkeley and UC Berkeley) is a major research university located in Berkeley 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. In Mathematics, a monopole is a connection over a Principal bundle G with a section (the Higgs field) of the associated In Mathematics, a 3-manifold is a 3-dimensional Manifold. The topological Piecewise-linear, and smooth categories are all equivalent in three dimensions Clifford Henry Taubes is a professor of mathematics at Harvard who works in gauge field theory and Differential geometry. He received his Ph. D. (Dr. phil. ) at Bochum in 1984, under the supervision of Eduard Zehnder.

Floer’s first pivotal contribution was a solution of a special case of Arnold's conjecture on fixed points of a symplectomorphism. Vladimir Igorevich Arnol'd or Arnold (Влади́мир И́горевич Арно́льд born June 12, 1937 in Odessa, Ukrainian SSR In Mathematics, a symplectomorphism is an Isomorphism in the category of Symplectic manifolds Formal definition Specifically In Mathematics, a symplectomorphism is an Isomorphism in the category of Symplectic manifolds Formal definition Specifically 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. Floer homology is a mathematical tool used in the study of Symplectic geometry and low-dimensional Topology. The International Congress of Mathematicians (ICM is the largest congress in the Mathematics community (IPA /kʲoːto / is a city in the central part of the island of Honshū, Japan. He received a Sloan Fellowship in 1989. The Sloan Research Fellowships are awarded annually by the Alfred P

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 unanticipated sudden suicide in 1991.

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. Simon Kirwan Donaldson (born August 20 1957 in Cambridge, England) is an English mathematician famous for his work on the Topology of . . . 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

Further reading

Posthumous publications

External links

Footnotes

  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])
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