Viktor Ginzburg

Viktor Ginzburg
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

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.

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

^ 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 $C^{2}$ -smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb {R} ^{4}$ ", 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

External links

Viktor Ginzburg at the Mathematics Genealogy Project

[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 $C^{2}$ -smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb {R} ^{4}$ ", Annals of Mathematics, 2, 158 (3): 953–976, arXiv:math.DG/0110047, doi:10.4007/annals.2003.158.953, MR 2031857, S2CID 7474467

[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, S2CID 18496888

[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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Authority control databases
International	ISNI VIAF
National	Germany Israel
Academics	Mathematics Genealogy Project zbMATH MathSciNet
Other	IdRef