VIKTOR L. GINZBURG Professor of Mathematics M.S., Moscow Institute of Steel and Alloys Ph.D., University of California, Berkeley My Page Selected Publications Curriculum Vitae

Phone: 831-459-2218 Office: Baskin 353C Office Hours: By Appt. Email: ginzburg@ucsc.edu

RESEARCH INTERESTS

Viktor Ginzburg's research interest has been in various areas of global analysis. These areas are symplectic topology and Hamiltonian dynamics, Poisson Lie groups and Poisson manifolds, and Hamiltonian actions of Lie groups.

1. Ginzburg's research in symplectic topology and Hamiltonian dynamics focuses on the existence problem for periodic orbits of certain Hamiltonian systems. Hamiltonian systems without periodic orbits and the systems describing the motion of a charge in a magnetic field are his primary concern.

2. The geometry of Poisson Lie groups and Poisson manifolds is known to be strongly related to both the theory of quantum groups and deformation quantization. Ginzburg is interested in the explicit calculation of certain invariants of Poisson manifolds and the study of momentum mappings for Poisson Lie groups.

3. Applications of cobordism techniques to gain a new understanding of various "classic" and recent results in symplectic geometry is the center of his project undertaken jointly with V. Guillemin (MIT) and Y. Karshon (Hebrew University). The examples of such applications are new proofs of the Duistermaat-Heckman formula, the Jeffrey-Kirwan localization theorem, and the fact that geometric quantization commutes with reduction.

SELECTED PUBLICATIONS (Complete List)

V.L. Ginzburg, V. Guillemin, and Y. Karshon: Cobordisms and Hamiltonian group actions. Mathematical Surveys and Monographs, vol.98. American
Mathematical Society, (2002). Link to the AMS Bookstore.  

V.L. Ginzburg and B. Gruel: Local Floer Homology and the Action Gap. Preprint, arXiv:0709.4077 (2007).

V.L. Ginzburg and B. Gruel: Periodic Orbits of Twisted Geodesic Flows and the Weinstein-Moser Theorem. Preprint, arXiv:0705.1818. Comment. Math. Helv (2007).

V.L. Ginzburg: Coisotropic Intersections. math. SG/0605186. Duke Mathematical J (2007), 140:111-163.

V.L. Ginzburg: The Conley conjecture. Preprint, math.SG/0610956 (2006).

V.L. Ginzburg: The Weinstein conjecture and the theorems of nearby and almost existence. math.DG/0310330. The Breadth of Symplectic and Poisson Geometry. Festschrift in Honor of Alan Weinstein, Editors J.E. Marsden and T.S. Ratiu. Birkhauser (2005), 139-172.

V.L. Ginzburg and B. Gruel: Relative Hofer-Zehnuder capacity and periodic orbits in twisted cotangent bundles. math.DG/0301073. Duke Mathematical J 123 (2004), 1-47.

V.L. Ginzburg and B. Gruel: On the construction of a C2-counterexample to the Hamiltonian Seifert Conjecture in R4. math.DG/0110047.  Ann. of Math 158 (2003), 953-976.

V.L. Ginzburg and E. Kerman: Periodic orbits of Hamiltonian flows near symplectic extrema. math.DG/0011011. Pacific J. Math (2002), 206:69-91.

V.L. Ginzburg: An embedding S->R, 2n-17, whose Hamiltonian flow has no periodic trajectories, IMRN 2 (1995), 83-98.

V.L. Ginzburg and A. Weinstein: Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc 5 (1992), 445-453.

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