Viktor L. Ginzburg is a Russian-American
mathematician who has worked on
Hamiltonian dynamics and
symplectic and
Poisson geometry
In differential geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M , subject to the Leibniz rule
: \ = \h + g \ .
Equivalen ...
. 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
The Conley conjecture, named after mathematician Charles Conley, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry.
Background
Let (M, \omega) be a compact symplectic manifold. A vector field V ...
, 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 which constructs a Hamiltonian with an energy level with no periodic trajectories.
Some of his other works concern coisotropic
intersection theory, and
Poisson–Lie groups.
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".
References
External links
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{{DEFAULTSORT:Ginzburg, Viktor
Living people
1962 births
20th-century Russian mathematicians
21st-century Russian mathematicians
University of California, Santa Cruz faculty
University of California, Berkeley alumni
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society