Andreas Floer (; 23 August 1956 – 15 May 1991) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who made seminal contributions to

symplectic topology Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Ha ...

, and

mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developme ...

, in particular the invention of

Floer homology In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer in ...

. Floer's first pivotal contribution was a solution of a special case of Arnold's conjecture on fixed points of a

symplectomorphism 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 sy ...

. 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 Kyoto (; Japanese language, Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin, Keihanshin metropolitan area along wi ...

in August 1990. He received a

Sloan Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

in 1989.

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 The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, living at Barrington Hall of the Berkeley Student Cooperative, and undertook Ph.D. work on monopoles on

3-manifold In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds lo ...

s, under the supervision of

Clifford Taubes Clifford Henry Taubes (born February 21, 1954) is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology. His brother is the journalist Gary Taube ...

; but he did not complete it when interrupted by his obligatory

alternative service Alternative civilian service, also called alternative services, civilian service, non-military service, and substitute service, is a form of national service performed in lieu of military conscription for various reasons, such as conscientious ...

in Germany. 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.

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 Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. H ...

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

*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

# 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.
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.
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

References

External links

* *
The In Memoriam website of the Department of Mathematics at the University of California, Berkeley
* ttp://texts.cdlib.org/xtf/view?docId=hb7c6007sj&doc.view=frames&chunk.id=div00018&toc.depth=1&toc.id= Elaborate obituary by Addison/Casson/Weinstein at OAC, Online Archive of California, 1992* For images, se
Wikimedia Commons Andreas Floer
an
a public Andreas Floer photo album on Facebook

(access forbidden; 2021-Jul-16)
YouTube alternative

Introduction to Floer Theory. Lecture by Dusa McDuff 2010

Introduction to Floer Theory? at mathoverflow.net
{{DEFAULTSORT:Floer, Andreas Topologists 1956 births 1991 suicides University of California, Berkeley alumni University of California, Berkeley faculty 20th-century German mathematicians Suicides in Germany Berkeley Student Cooperative alumni