Viktor Ginzburg

Viktor Ginzburg
Viktor Ginzburg at Oberwolfach in 2008
Nationality United States
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

Viktor L. Ginzburg is a Russian-American mathematician who has worked on Hamiltonian dynamics and symplectic and Poisson geometry.

Ginzburg 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.

He 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 more influential works concern coisotropic intersection theory,[3] and Poisson Lie groups.[4]

As of 2017, Ginzburg is Professor of Mathematics at the University of California, Santa Cruz.

References

  1. ↑ 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
  2. ↑ 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
  3. ↑ 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
  4. ↑ V. Ginzburg and A. Weinstein, Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc. (2) 5, 445-453, 1992.
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