Nikolay Nessonov

Division of Mathematics

B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine

47 Nauky ave. Kharkiv, 61103, UKRAINE

Date of Birth:

 

January

 

2, 1954

Citizenship:

 

Ukrainin

 

 

Education:

 

M.S.

 

Faculty of Mechanics and Mathematics, Kharkiv National University, June, 1976;

Ph.D.

 

Kharkiv National  University, June 6, 1980.  Title: " Automorphisms of hyperfinite factors and some questions of noncommutative ergodic theory ". Supervisor V. Ya. Golodets

 

D.Sc.

 

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, June 19, 2007. Title: "Classification of the representations of infinite dimensional matrix groups and automorphisms of operator algebras". 

Permanent Positions:

 

 

01.2009 till now

 

Leading Research Fellow,  Division of Mathematics, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

 

06.200212.2008

 

Senior Research Fellow, Division of Mathematics, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

 

08.198502.2002

 

Assotiate Professor, Dept. of Higher Mathematics, Kharkiv National Technical University of Agriculture

01.198008.1985

 

Senior lecturer,  Dept. of Higher Mathematics, Kharkiv National Technical University of Agriculture

 

Research interests:

Representations Theory:

Representations of the operator algebras, infinite dimensional matrix group, infinite symmetrical group.

List of principal publications

  1. Nikolay Nessonov, Nhok Tkhai Shon Ngo, Indecomposable characters of inductive limits
    of symmetric groups, Represent. Theory 29 (2025), 256-288; DOI:https://doi.org/10.1090/ert/689

  2. Nessonov N.I., Sinel'shchikov S. D., An Analogue of the Schur-Weyl Duality for the Automorphism Group of a II1 -Factor, Journal of Lie Theory 34 (2024), No. 3, 611—638.

  3. Nessonov N. I., Characters of the Infinite Symmetric Inverse Semigroup,  Functional Analysis and Its Applications, Volume 54, pages 179–187, (2020).

  4. Nessonov N.I., A Nonsingular Action of the Full Symmetric Group Admits an Equivalent Invariant Measure, Æóðí. ìàò. ô³ç. àíàë. ãåîì. 16 (2020), 46-54, doi: https://doi.org/10.15407/mag16.01.046

  5. Íåññîíîâ Í.È., Àíàëîã äâîéñòâåííîñòè Øóðà–Âåéëÿ äëÿ óíèòàðíîé ãðóïïû II_1-ôàêòîðà , Ìàòåì. ñá., 2019,  òîì 210, íîìåð 3, ñòð. 162–188 (Mi msb8986),
     http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=8986&option_lang=rus

  6. Vershik A.M., Nessonov N. I., Stable representations of the infinite symmetric group, Izvestiya: Mathematics(2015),79(6):1184-1214.

  7. Nessonov N. I., KMS states on S∞ invariant with respect to the Young subgroups (in russian), Funktsional. Anal. I Prilozhen, 47 (2013), no.2, 55--67; translation in  Funct. Anal. Appl.  47 (2013), no. 2, 127–137

  8. Nessonov N. I., On realizations of representations of the infinite symmetric group (in russian) , Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 403 (2012), Teoriya Predstavleniĭ, Dinamicheskie Sistemy, Kombinatornye Metody. XXI,  110--117,199;translation in J. Math. Sci. (N.Y.) 190 (2013), no. 3, 468–471.

  9. Nessonov N. I., Stable states and representations of the infinite symmetric group (in russian),  Dokl. Akad. Nauk  445 (2012), no. 1, 9--12; translation in  Dokl. Math.  86 (2012), no. 1, 450–453.

  10. Nessonov N. I., Representations of S∞ admissible with respect to Young subgroups (in russian),  Mat. Sb. 203 (2012), no. 3, 127--160; translation in Sb. Math. 203 (2012), no. 3-4, 424–458.

  11. Dudko, A. V., Nessonov N. I., Characters of projective representations of the infinite generalized symmetric group  (in russian),  Mat. Sb. 199 (2008), no. 10, 3--32;  translation inSb. Math. 199 (2008), no. 9-10, 1421–1450.

  12. Dudko, A. V., Nessonov N. I., Projective characters of the infinite generalized symmetric group (in russian), Funktsional. Anal. I Prilozhen. 42 (2008), no.1, 82--85; translation in Funct. Anal. Appl. 42 (2008), no. 1, 69–71.

  13. Dudko, A. V., Nessonov N. I., A description of characters on the infinite wreath product,  Methods Funct. Anal. Topology 13 (2007), no. 4, 301–317.

  14. Nessonov N. I., Kubo-Martin-Schwinger states on the group GL(∞) and admissible representations of GL(∞)^X, Proceedings of the St. Petersburg Mathematical Society. Vol. X, 109–165, Amer. Math. Soc., Transl. Ser. 2, 214, Amer. Math. Soc., Providence, RI, 2005.

  15. Boyko M.S., Nessonov N. I., Entropy of the shift on II1-representations of the group S(∞), Ukr. Mat. Visn.  2 (2005), no. 1, 15--37; translation in  Ukr. Math. Bull.  2 (2005), no. 1, 15–37.

  16. Boyko M.S., Nessonov N. I.., Entropy of Bogoliubov automorphisms on II_1 representations of the group U(∞), Methods Funct. Anal. Topology 9 (2003), no. 4, 317–332.

  17. Nessonov N. I., Factor representations of the group GL(∞) and admissible representations of GL(∞)^X (in russian),  Mat. Fiz. Anal. Geom.11(2004), no.1, 67–86.

  18. Nessonov N. I., Complete classification of admissible representations of infinite-dimensional classical matrix groups.II (in russian), Mat. Fiz. Anal. Geom. 9 (2002), no. 1, 79–94.

  19. Nessonov N. I., Complete classification of admissible representations of infinite-dimensional classical matrix groups,.I (in russian),  Mat. Fiz. Anal. Geom. 8 (2001), no. 3, 282–307.

  20. Nessonov N. I., Representations of infinite-dimensional matrix groups and associated dynamical systems, Operator algebras and operator theory (Craiova, 1989), 157–167, Pitman Res. Notes Math. Ser.,271,  Longman Sci. Tech.,Harlow, 1992.

  21. Nessonov N. I., Representations of a group of invertible infinite matrices with coefficients in a finite-dimensional algebra. (Russian)  Funktsional. Anal. i Prilozhen., 26 (1992), no. 2, 93-- 95; transl. in Funct. Anal. Appl. 26 (1992), no. 2, 151–153.

  22. Golodets V.Ya., Nessonov N. I.,T-property and nonisomorphic full factors of types II and III,. J. Funct. Anal. 70 (1987), no.1, 80–89.. 

  23. 18.Nessonov N. I., Complete classification of representations of GL(∞) containing the identity representation of the unitary subgroup (in russian),  Mat. Sb. (N.S.) 130(172) (1986), no. 2, 131--150, 284; translation in Math. USSR-Sb. 58 (1987), no.1,127–147

  24. Nessonov N. I., Examples of factor-representations of the group GL(∞).(in russian) , Mathematical physics, functional analysis (in russian), 48–52, 144, Naukova Dumka, Kiev,1986.

  25. Gefter S.L., Golodets V.Ya., Nessonov N. I., Actions of T-groups on von Neumann algebras with countable fundamental groups (in russian),  Funktsional. Anal. i Prilozhen.  19(1985), no. 1, 64–65.

  26. Matveichuk M.S., Nessonov N. I., Description of finite measures in von Neumann factors of type III. (in russian)  Izv. Vyssh. Uchebn. Zaved. Mat. 1984, no. 2, 68–71.

  27. Nessonov N. I., Description of representations of the group of invertible operators in a Hilbert space, containing the identity representation of the unitary subgroup (in russian),   Funktsional. Anal. I Prilozhen.  17 (1983), no. 1, 79–80.

  28. Nessonov N. I., Structure of factors of the type III_λ (0<λ≤1) (in russian), Funk. Anal. i Prilozhen.  14 (1980), no. 3, 89–90.

  29. Golodets V.Ya., Nessonov N. I., Asymptotic algebra and outer conjugacy classes of automorphisms of factors (in russian),  Izv. Akad. Nauk SSSR Ser. Mat.  44 (1980), no.3, 510–532.

  30. Golodets V.Ya., Nessonov N. I., Invariant states on asymptotically abelian factors of type III (in russian) , Funktsional. Anal. I Prilozhen.  13 (1979), no. 2, 81–82.

Recent CONFERENCES 

Dynamics,Combinatorics,Representations, 31/8-4/9, 2015 at the Euler Institute, St.Petersburg.

Function theory and dynamics of point processes , 1/6-3/6, 2017 at the Euler Institute, St.Petersburg.