Viktor Ginzburg

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.

Not to be confused with Victor Ginzburg, Victor Ginzburg (director), or Victor Ginsburgh.
Viktor Ginzburg
Viktor Ginzburg at Oberwolfach in 2008
NationalityUnited States
Alma materUniversity of California, Berkeley
Known forProof of the Conley conjecture
Counter-example to the Hamiltonian Seifert conjecture
Scientific career
FieldsMathematics
InstitutionsUniversity of California, Santa Cruz
Doctoral advisorAlan Weinstein

Education

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.

Research

Ginzburg 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

Ginzburg 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
  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.
  5. 2020 Class of the Fellows of the AMS, American Mathematical Society, retrieved 2019-11-03
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