Andreas Floer

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Andreas Floer
Andreas Floer 1976.JPG
Andreas Floer in 1975
Born(1956-08-23)August 23, 1956
DiedMay 15, 1991(1991-05-15) (aged 34)
Nationality German
Alma mater Ruhr-Universität Bochum
Known for Floer homology
Scientific career
Fields Mathematics
Institutions Ruhr-Universität Bochum
University of California, Berkeley
Doctoral advisor Eduard Zehnder
Ralf Stöcker

Andreas Floer (German: [ˈfløːɐ] ; 23 August 1956 – 15 May 1991) was a German mathematician who made seminal contributions to the areas of geometry, topology, and mathematical physics, in particular the invention of Floer homology.

Germany Federal parliamentary republic in central-western Europe

Germany, officially the Federal Republic of Germany, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north, and the Alps to the south. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, France to the southwest, and Luxembourg, Belgium and the Netherlands to the west.

Mathematician person with an extensive knowledge of mathematics

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

Geometry branch of mathematics that measures the shape, size and position of objects

Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

Contents

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 and undertook PhD 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. He received his PhD (Dr. phil.) at Bochum in 1984, under the supervision of Eduard Zehnder.

A Diplom is an academic degree in the German-speaking countries Germany, Austria, and Switzerland and a similarly named degree in some other European countries including Bulgaria, Belarus, Bosnia and Herzegovina, Croatia, Estonia, Finland, Poland, Russia, and Ukraine and only for engineers in France, Greece, Hungary, Romania, Serbia, Macedonia, Slovenia, and Brazil.

University of California, Berkeley Public university in California, USA

The University of California, Berkeley is a public research university in the United States. Located in the city of Berkeley, it was founded in 1868 and serves as the flagship institution of the ten research universities affiliated with the University of California system. Berkeley has since grown to instruct over 40,000 students in approximately 350 undergraduate and graduate degree programs covering numerous disciplines.

In mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle.

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.

In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation.

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).

Kyoto Designated city in Kansai, Japan

Kyoto, officially Kyoto City, is the capital city of Kyoto Prefecture, located in the Kansai region of Japan. It is best known in Japanese history for being the former Imperial capital of Japan for more than one thousand years, as well as a major part of the Kyoto-Osaka-Kobe metropolitan area.

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.

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."

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" and "the full richness of Floer's theory is only beginning to be explored".

"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."

Selected publications

Posthumous publications

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 ()

Further reading

Related Research Articles

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