Viktor L. Ginzburg is a Russian-American mathematician who has worked on Hamiltonian dynamics and symplectic and Poisson geometry. As of 2017, Ginzburg is Professor of Mathematics at the University of California, Santa Cruz.
Viktor Ginzburg | |
|---|---|
 Viktor Ginzburg at Oberwolfach in 2008 | |
| Born | 1962 |
| Nationality | American |
| Alma mater | University of California, Berkeley |
| Known for | Proof of the Conley conjecture Counter-example to the Hamiltonian Seifert conjecture |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of California, Santa Cruz |
| Doctoral advisor | Alan Weinstein |
Education
editGinzburg completed his Ph.D. at the University of California, Berkeley in 1990; his dissertation, On closed characteristics of 2-forms, was written under the supervision of Alan Weinstein.
Research
editGinzburg is best known for his work on the Conley conjecture,[1] which asserts the existence of infinitely many periodic points for Hamiltonian diffeomorphisms in many cases, and for his counterexample (joint with Başak Gürel) to the Hamiltonian Seifert conjecture[2] which constructs a Hamiltonian with an energy level with no periodic trajectories.
Some of his other works concern coisotropic intersection theory,[3] and Poisson–Lie groups.[4]
Awards
editGinzburg was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to Hamiltonian dynamical systems and symplectic topology and in particular studies into the existence and non-existence of periodic orbits".[5]
References
edit- ^ Ginzburg, Viktor L. (2010), "The Conley conjecture", Annals of Mathematics, 2, 172 (2): 1127–1180, arXiv:math/0610956, doi:10.4007/annals.2010.172.1129, MR 2680488
- ^ Ginzburg, Viktor L.; Gürel, Başak Z. (2003), "A -smooth counterexample to the Hamiltonian Seifert conjecture in ", Annals of Mathematics, 2, 158 (3): 953–976, arXiv:math.DG/0110047, doi:10.4007/annals.2003.158.953, MR 2031857, S2CID 7474467
- ^ Ginzburg, Viktor L. (2007), "Coisotropic intersections", Duke Mathematical Journal, 140 (1): 111–163, arXiv:math/0605186, doi:10.1215/S0012-7094-07-14014-6, MR 2355069, S2CID 18496888
- ^ V. Ginzburg and A. Weinstein, Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc. (2) 5, 445-453, 1992.
- ^ 2020 Class of the Fellows of the AMS, American Mathematical Society, retrieved 2019-11-03
