
Most recent papers

Classification of finite metric spaces and combinatorics of convex polytopes.
To appear in Arnold Math. J.

The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra
$\widehat{sl}_2$ (with N.V.Tsilevich).
Lett. Math. Phys. 105, No. 1, 1125 (2015).

Virtual continuity of measurable functions and
its applications (with P.B.Zatitskiy and F.V.Petrov).
Uspekhi Mat. Nauk 69, No. 6, 81114 (2014).

The problem of describing central measures on the path spaces of graded graphs.
Funct. Anal. Appl. 48, No. 4, 120 (2014).

Cohomology in nonunitary representations of semisimple Lie groups (the group U(2,2)) (with
M.I.Graev).
Funct. Anal. Appl. 48, No. 3, 113 (2014).

About A.N.Livshits (in Russian).
In: A.N.Livshits, Dynamical Systems, Ergodic Theory, Formal Languages (A.A.Lodkin, ed.). St.Petersburg, 2014.

MongeKantorovich problem along years.
In: Advances in Economics and Optimization,
D.Wingkay Yeung et al. (eds.), Nova Science Publishers (2014),
Chapter 2, pp. 718.

Gromov's geometry.
In: The Abel Prize 20082012, H.Holden and R.Piene (eds.), Springer
(2014), pp.143148.

Intrinsic metric on graded graphs, standardness, and invariant
measures.
Zapiski Nauchn. Semin. POMI 421, 5867 (2014).

Finite traces and representations of the group of infinite matrices
over a finite field
(with V.Gorin and S.Kerov).
Adv. in Math. 254, 331395 (2014).

Infinitedimensional SchurWeyl duality and the CoxeterLaplace operator
(with
N.V.Tsilevich).
Comm. Math. Phys. 327, No. 3, 873885 (2014).
 Several thoughts about Arnold.
In: Arnold: Swimming Against the Tide (B.A.Khesin and S.L.Tabachnikov, eds.). Amer. Math. Soc., 2014, pp. 187196.
The Russian version.

Virtual continuity of measurable functions of several variables and
embedding theorems (with P.B.Zatitskiy and F.V.Petrov).
Funct. Anal. Appl. 47, No. 3, 165173 (2013).

Long history of
the MongeKantorovich transportation problem.
Math. Intelligencer 35, No. 4 (2013).

Special representations of nilpotent Lie groups and the associated
Poisson representations of current groups
(with
M.I.Graev).
Moscow Math. J. 13, No. 2, 345360 (2013).

New developments in the theory of metric spaces
(in Russian).
In: Proceedings of the Globus Seminar, Vol. 6, MCCME, Moscow (2013),
pp. 243272.

Smooth and nonsmooth AFalgebras and a problem on invariant measures.
To appear in Proceedings of the St. Petersburg School in Probability and
Statistical Physics (June 2012).

Two
ways to define compatible metrics on the simplex of measures.
Zapiski Nauchn. Semin. POMI 411, 3848 (2013).
 An interview for the Russian political news
channel polit.ru:
Part I, Part II (in Russian).

Between
"very large" and "infinite": the asymptotic representation theory.
Probability and Mathematical Statistics, 33, Fasc. 2,
467476 (2013).

Geometry and dynamics of admissible metrics in measure spaces
(with
F.Petrov and P.Zatitskiy).
Central Europ. J. Math. 11, No. 3, 379400 (2013).

Gelfand, My Inspiration.
Notices AMS, 60, No. 1, 3238 (2013).

Nonsingular transformations of the symmetric Levy processes
(with N.V.Smorodina),
Zapiski Nauchn. Semin. POMI 408, 102114 (2012). English version
to appear in J. Math. Sci.

On classification of measurable functions of several variables,
Zapiski Nauchn. Semin. POMI 403, 3557 (2012). English version
to appear in J. Math. Sci.190, No. 3 (2013).

Leonid Vital'evich Kantorovich (on the 100th anniversary of his birth)
(with S.S.Kutateladze and S.P. Novikov).
Russian Math. Surveys 67, No. 3, 589 (2012).
Russian
preprint version.

Representation of the infinitedimensional groups of rank one
(with
M.I.Graev).
Moscow Math. J. 12, No. 3, 117129 (2012).
ArXiv version.

C^*algebras associated with endomorphisms and polymorphisms of compact
abelian groups
(with
J.Cuntz).
Comm. Math. Phys. 321, No. 1, 157179 (2013).

Special representations of the groups
U(∞,1) and O(∞,1) and
related representations of the current groups U(∞,1)^{X} and
O(∞,1)^{X}
in a quasiPoisson space
(with
M.I.Graev).
Funct. Anal. Appl. 46, No. 1, 110 (2012).

Stable states and representations of the infinite symmetric group (with
N.I.Nessonov).
Dokl. Math. 86, No. 1, 450453 (2012).

Totally nonfree actions and the infinite
symmetric group.
Moscow Math. J. 12, No. 1, 193212 (2012).
