
Most recent papers

Three theorems on the uniqueness of a Plancherel measure from different viewpoints.
To appear in Trudy MIAN (2019).

The absolute of finitely generated groups: I. Commutative (semi)groups (with
A.V.Malyutin).
European J. Math. 4, No. 4, 14791490 (2018).

The asymptotic behavior of the number of geodesics in the discrete Heisenberg group
(with A.V.Malyutin).
Zapiski Nauchn. Semin. POMI 468, 3952 (2018).

On a universal Borel adic space (with P.B.Zatitskii).
Zapiski Nauchn. Semin. POMI 468, 2438 (2018).

Combinatorial invariants of metric filtrations and automorphisms; the universal adic graph (with P.B.Zatitskii).
Funct. Anal. Appl. 52, No. 4, 2337 (2018).

The absolute of finitely generated groups: II. The Laplacian part and degenerate part (with
A.V.Malyutin).
Funct. Anal. Appl. 52, No. 3, 321 (2018).

On the decomposition of tensor representations of symmetric groups (with
P.P.Nikitin and N.V.Tsilevich).
To appear in Algebras and Representation Theory (2018).

Corrigendum to the paper "A new approach to the representation theory of the symmetric groups. IV. Z2graded groups and algebras"
(with A.Sergeev).
Moscow Math. J. 18, No. 1, 187 (2018).

Infinite geodesics in the discrete Heisenberg group
(with A.V.Malyutin).
Zapiski Nauchn. Semin. POMI 462, 3951 (2017).

Nonunitary representations of the groups of U(p,q)currents for q ≥ p>1
(with M.I.Graev).
Zapiski Nauchn. Semin. POMI 462, 538 (2017).

Duality and free measures in vector spaces; spectral theory and
the actions of non locally compact groups.
Zapiski Nauchn. Semin. POMI 457, 74100 (2017).

Universal adic approximation, invariant measures and scaled entropy (with P.B.Zatitskiy).
Izv. Math.
81, No. 4, 734770 (2017).

The theory of filtrations of subalgebras, standardness, and independence.
Russian Math. Surveys
72, No. 2, 257333 (2017).

Does a freedom of the choice exist in mathematics?
In: Proceedings of the International Conference "Philosophy, Mathematics, Linguistics: Aspects of Interaction", St.Petersburg, 2014.

About Grisha Mints,
IfColog Journal of Logics and Their Applications
4, No. 42017, 841843.

An interview for the magazine "Ogonyok"
(in Russian),
Ogonyok, No. 4(5451), January 30, 2017, pp. 2830.

On the relation of some combinatorial functions to representation theory
(with N.V.Tsilevich).
Funct. Anal. Appl. 51, No. 1, 2839 (2017).

Universal adic approximation, invariant measures and scaling entropy
(with P.B.Zatitskiy).
PDMI Preprint 06/2016 (2016).

Special representations of Iwasawa subgroups of simple Lie groups
(with M.I.Graev).
Zapiski Nauchn. Semin. POMI 448, 96106 (2016).

Asymptotic theory of path spaces of graded
graphs and its applications.
Japanese J. Math. 11, No. 2, 151218 (2016).

Laplace operators in gamma analysis (with D.Hagedorn, Yu.Kondratiev, and E.Lytvynov).
In: Stochastic and Infinite Dimensional Analysis. Trends in Mathematics, C.C.Bernido et al. (eds.), Springer, 2016, pp. 119147.

Smoothness and standardness in the theory of AFalgebras and in the problem on invariant measures.
In: Probability and Statistical Physics in St. Petersburg, V.Sidoravicius and
S.Smirnov (eds.), Proceedings of Symposia in Pure Mathematics 91, Amer. Math. Soc. (2016), pp. 430443.

Several remarks on Pascal automorphism and infinite ergodic theory.
Armenian J. Math. 7, No. 2, 8596 (2015).

Equivalence of the Brownian and energy representations (with S.Albeverio, B.K.Driver, M.Gordina).
Zapiski Nauchn. Semin. POMI 441, 1744 (2015).

Integration of virtually continuous functions over bistochastic measures and the trace formula for nuclear operators (with P.B.Zatistkiy and F.V.Petrov),
Algebra i Analiz 27, No. 3, 6674 (2015).

Invariant measures: new aspects of dynamics, combinatorics and representation theory.
In: The Fifteenth Takagi Lectures, 2728 June 2015, Tohoku, The Mathematical Society of Japan, 2015, ISSN 21873267, pp. 3979.

On the classification problem of matrix distributions of measurable functions in several variables (with U.Haboeck).
Zapiski Nauchn. Semin. POMI 441, 119143 (2015).
 Cohomology of the Iwasawa subgroup of the group U(p,p) in nonunitary representations
(with M.I.Graev).
Zapiski Nauchn. Semin. POMI 436, 112121 (2015).
English translation to appear in J. Math. Sci. (N.Y.).

Standardness as an invariant formulation of independence.
Funct. Anal. Appl. 49, No. 4, 1833 (2015).

Laplace operators on the cone of Radon measures (with Yu.Kondratiev and E.Lytvynov).
J. Funct. Anal. 269, No. 9, 29472976 (2015).

Several words about Mikhail Iosifovich Gordin [in Russian].
Zapiski Nauchn. Semin. POMI 441, 911 (2015).

Stable representations of the infinite symmetric group [in Russian] (with
N.I.Nessonov).
Izv. RAN. Ser. Mat. 79, No. 6, 93124 (2015).

Phase transition in the exit boundary problem for random walks on groups (with
A.V.Malyutin).
Funct. Anal. Appl. 49, No. 2, 8696 (2015).

Equipped graded graphs, projective limits of simplices, and their boundaries.
Zapiski Nauchn. Semin. POMI 432, 83104 (2015).
English translation to appear in J. Math. Sci.

Classification of finite metric spaces and combinatorics of convex polytopes.
Arnold Math. J. 1, No. 1, 7581 (2015).

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.

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).

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