Helmut H. Hofer

Hofer is one of the founders of the modern field of Symplectic Topology. He has made fundamental contributions to Hamiltonian Mechanics, Symplectic Geometry and related analysis and geometry. Among his many achievements is his work on symplectic capacities with I. Ekeland and  E. Zehnder related to rigidity phenomena of symplectic maps,  his early breakthroughs on the Arnold conjectures, his joint works with Floer and others on Symplectic Homology theory, his bi-invariant metric on the group of Hamilton Diffemorphisms (leading to "Hofer Geometry" ), his introduction of holomorphic curves into contact geometry and with it the solution of some fundamental cases of the Weinstein Conjectures concerning periodic orbits,  as well as the development of Symplectic Field Theory jointly with Y. Eliashberg and A. Givental. He introduced with K. Wysocki and E. Zehnder the theory of finite energy foliations and with J. Fish the theory of Feral Curves.  Finally, with K. Wysocki and E. Zehnder he introduced Polyfold Theory to give rigorous foundations for  constructing  "Floer-like" theories.