Person: Floer, Andreas
Andreas Floer was a German mathematician best known for his work in symplectic topology and mathematical physics.
Mathematical Profile (Excerpt):
- Floer was appointed as a research assistant at the University of California at Berkeley and he returned to the United States in early 1985 to take up the appointment.
- Back in Berkeley he began to develop a fundamental theory which is now named Floer homology.
- Floer obtained a postdoctoral fellowship in mathematical physics at the State University of New York at Stony Brook where he worked for a year before being appointed Courant Instructor at New York University where he spent the following two years.
- Floer developed a new method for "counting" the solutions of maximum-minimum problems arising in geometry.
- Andreas realized that the difference between the indices of any two solutions could still be defined and could be used where the index itself was useless.
- Combining this observation with detailed, careful analysis, and using work of many other mathematicians as well as his own, Andreas developed a theory that led to the solution of a number of outstanding problems.
- The value of his work was grasped immediately by specialists in differential geometry, topology, and mathematical physics, for whom "Floer homology" has become an essential part of their problem-solving toolkit.
- In 1987 Floer published Morse theory for fixed points of symplectic diffeomorphisms in the Bulletin of the American Mathematical Society.
- After reviewing Morse theory in finite dimensions, Floer went on to outline applications to symplectic geometry, working on the loop space on a symplectic manifold.
- In particular he looks there at Floer's progress on the Arnol'd conjecture and instanton homology, and at Floer's instanton homology and 4-dimensional cobordisms.
Born 23 August 1956, Duisburg, Germany. Died 15 May 1991, Bochum, Germany.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive