VERSHIK, ANATOLY / Mathematics / Researchers

International Center for Scientific Research

Researchers

Mathematics / VERSHIK, ANATOLY

vershikpdmi.ras.ru

Position

Head of the Laboratory of Representation Theory and Computational Mathematics,
St.Petersburg Department of Steklov Institute of Mathematics,
St.Petersburg, Russia.

Professor of the Chair of Mathematical Analysis,
Department of Mathematics and Mechanics,
St.Petersburg State University.

Research interests

- ergodic theory, dynamical systems, symbolic dynamics, nonholonomic dynamics
- representation theory and its applications, asymptotic representation theory, infinite-dimensional groups, C*-algebras
- combinatorics, symmetric groups, approximations in algebra
- measure theory, statistics and asymptotics in combinatorics
- convex geometry, discrete geometry, subriemannian geometry
- linear and nonlinear programming, optimization.

Prizes and awards

President of the St.Petersburg Mathematical Society
Humboldt Research Award, 2008

Publications

Towards the definition of metric hyperbolicity.
To appear.

On different models of representations of the infinite symmetric group (with N.V.Tsilevich).
To appear.

On the Fourier transform on the infinite symmetric group (with N.V.Tsilevich).
Zapiski Nauchn. Semin. POMI 325 (2005).

How does a typical Markov operator look like?
PDMI preprint 06/2005 (in Russian). To appear in Algebra i Analiz.

The basic representation of the current group O(n,1)^X in the L^2 space over the generalized Lebesgue measure (with M.I.Graev).
To appear in Indag. Math.

On representations of groups of SO(n,1) currents (with M.I.Graev).
Funkts. Anal. Prilozh. 39, No. 2, 1-12 (2005).

Universality and randomness for the graphs and metric spaces.
To appear in \\\"Frontiers in Number Theory, Physics and Geometry\\\", Vol. 1: On random matrices, zeta functions and dynamical systems. Springer, 2005.

Gelfand-Tsetlin algebras, expectations, inverse limits, Fourier analysis.
To appear in \\\"Unity of Mathematics. Proc. of the conference in honor of the ninetieth birthday of I.M.Gelfand\\\", Birkhauser.

Polymorphisms, Markov processes, and quasi-similarity.
Discrete Contin. Dyn. Syst. 13, No. 5, 1305-1324 (2005).

Some isometry groups of Urysohn spaces (with P.Cameron).
To appear in J. of Pure and Appl. Logic.

C*-Algebras of irreversible dynamical systems (with R.Exel).
To appear in Canad. J. Math.

Geometrical approach to the free solvable groups (with S.V.Dobrynin).
To appear in Internat. J. Algebra Comput.

Alexandrov\\\'s inequality. Alexander Danilovich as I knew him (in Russian).
St.Petersburg University, No. 3-4 (2004), 36-40.

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