Eliashberg, Yakov, Kolokvij september 2016

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Symplectic topology was conceived by H. Poincare as a tool to answer qualitative problems of Classical Mechanics. The so-called "last geometric theorem" of Poincare, proven by G. Birkhoff in 1912 after Poincare’s death, can be viewed as the first result of symplectic topology. But the further development had to wait till the late 1960s, when V.I. Arnold formulated his famous conjectures. With the introduction by M. Gromov in 1985 of his famous method of pseudo-holomorphic curves in symplectic manifolds the subject began unravelling with an exponential speed. In the talk I will discuss the subject and methods of symplectic topology in their historical development from the work of Henri Poincare to our days.

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