# Viktor Ginzburg

Title | Professor |

Division | Physical & Biological Sciences |

Department | PBSci-Mathematics Department |

Phone | 831-459-2218 |

FAX | 831-459-4511 |

Web Site | ginzburg.math.ucsc.edu |

Office | McHenry Building Room #4124 |

Campus Mail Stop | Mathematics Department |

1156 High Street Santa Cruz, CA 95064 |

### Research Interests

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.

### Biography, Education and Training

M.S., Moscow Institute of Steel and Alloys

Ph.D., University of California, Berkeley

### Selected Publications

- 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