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ICMAT Laboratory "Viktor Ginzburg"

ICMAT Laboratory “Viktor Ginzburg”


Viktor Ginzburg
Viktor Ginzburg is Professor of Mathematics at the University of California, Santa Cruz, since 2004. He received his PhD from the University of California, Berkeley, in 1990 under the supervision of Alan Weinstein, with a thesis entitled “On closed characteristics of two-forms”. He has worked in various areas of symplectic geometry. His current research lies at the interface of Symplectic Topology and Hamiltonian Dynamical Systems and focuses on the existence problem for periodic orbits of Hamiltonian systems. Among his recent results are:
-           Counterexamples to the Hamiltonian Seifert conjecture, [2,4].
-           Existence results for periodic orbits of a charge in a magnetic field, [6].
-           A work on symplectic topology of coisotropic submanifolds (coisotropic intersections and rigidity), providing a common framework for the Arnold conjecture and the Weinstein conjecture for hypersurfaces, [5].
-           The proof of Conley’s conjecture on the existence of periodic points of Hamiltonian diffeomorphisms for a wide class of symplectic manifolds, [7,8]. 

Selected publications of Viktor Ginzburg:
[1] Lie-Poisson structures on some Poisson Lie groups (with A. Weinstein). J. Amer. Math. Soc. 5 (1992) 445-453.
[2] The Hamiltonian Seifert conjecture: examples and open problems, Proceedings of the Third European Congress of Mathematics, Barcelona, 2000; Birkhauser, Progress in Mathematics, 202 (2001), vol. II, pp. 547-555.
[3] Cobordisms and Hamiltonian groups actions (with V. Guillemin and Y. Karshon). Mathematical Surveys and Monographs, vol. 98, American Mathematical Society, 2002.
[4] A C2-smooth counterexample to the Hamiltonian Seifert conjecture in R4 (with B.Z. Gurel). Ann. of Math. 158 (2003) 953-976.
[5] Coisotropic intersections. Duke Math. J. 140 (2007) 111-163.
[6] Periodic orbits of twisted geodesic flows and the Weinstein-Moser theorem (with B.Z. Gurel). Comment. Math. Helv. 84 (2009) 865-907.
[7] Action and index spectra and periodic orbits in Hamiltonian dynamics (with B.Z. Gurel). Geom. Topol. 13 (2009) 2745-2805.     
[8] The Conley conjecture. Ann. of Math. 172 (2010) 1127-1180.