Search for people, departments, or email addresses.
Physical & Biological Sciences Division
Mathematics Department
Professor
Faculty
Regular Faculty
McHenry Library
McHenry Building Room #4124
Mathematics Department
M.S., Moscow Institute of Steel and Alloys
Ph.D., University of California, Berkeley
Viktor Ginzburg has worked in various areas of symplectic geometry including Poisson geometry, geometry of Hamiltonian group actions, geometric quantization, and symplectic topology. 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.
- Existence results for periodic orbits of a charge in a magnetic field.
- 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.
- The proof of Conley’s conjecture on the existence of periodic points of Hamiltonian diffeomorphisms for a wide class of symplectic manifolds.
- V. L. Ginzburg: The Conley conjecture. Ann. of Math. 172 (2010) 1127-1180
- V. L. Ginzburg and B. Z. Gurel: Action and index spectra and periodic orbits in Hamiltonian dynamics. Geom. Topol. 13 (2009) 2745-2805
- V. L. Ginzburg and B. Z. Gurel: Periodic orbits of twisted geodesic flows and the Weinstein-Moser theorem. Comment. Math. Helv. 84 (2009) 865-907
- V. L. Ginzburg: Coisotropic intersections. Duke Math. J. 140 (2007) 111-163
- V. L. Ginzburg and B. Z. Gurel: A C2-smooth counterexample to the Hamiltonian Seifert conjecture in R4. Ann. of Math. 158 (2003) 953-976
- V. L. Ginzburg, V. Guillemin and Y. Karshon: Cobordisms and Hamiltonian groups actions. Mathematical Surveys and Monographs, vol. 98, American Mathematical Society, 2002
- V. L. Ginzburg: 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
This campus directory is the property of the University of California at Santa Cruz. To protect the privacy of individuals listed herein, in accordance with the State of California Information Practices Act, this directory may not be used, rented, distributed, or sold for commercial purposes. For more details, please see the university guidelines for assuring privacy of personal information in mailing lists and telephone directories. If you have any questions please contact the ITS Support Center.