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Tr. Mosk. Mat. Obs., 2020, Volume 81, Issue 2, Pages 145–203 (Mi mmo639)  

This article is cited in 1 scientific paper (total in 1 paper)

Applications of noncommutative geometry in function theory and mathematical physics

A. G. Sergeev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We review some applications of noncommutative geometry to function theory and mathematical physics. In the first case we discuss relations between the spaces of real variables and operator algebras. In the second case we deal with quantization of universal Techmüller space and quantum Hall effect.

Key words and phrases: operator calculus, Shatten–von Neumann classes, quantization of the universal Teichmüller space, quantum Hall effect.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00474
18-51-41011
18-51-05009
While preparing this paper the author was partially financially supported by the RFBR grants 19-01-00474, 18-51-41011, 18-51-05009.


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English version:
Transactions of the Moscow Mathematical Society, 2020, 81:2, 123–167

UDC: 517.986.9
MSC: 58B34, 81R60
Received: 11.04.2020
Revised: 29.04.2020

Citation: A. G. Sergeev, “Applications of noncommutative geometry in function theory and mathematical physics”, Tr. Mosk. Mat. Obs., 81, no. 2, MCCME, M., 2020, 145–203; Trans. Moscow Math. Soc., 81:2 (2020), 123–167

Citation in format AMSBIB
\Bibitem{Ser20}
\by A.~G.~Sergeev
\paper Applications of noncommutative geometry in function theory and mathematical physics
\serial Tr. Mosk. Mat. Obs.
\yr 2020
\vol 81
\issue 2
\pages 145--203
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo639}
\elib{https://elibrary.ru/item.asp?id=46761459}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2020
\vol 81
\issue 2
\pages 123--167
\crossref{https://doi.org/10.1090/mosc/307}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85103160875}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Sergeev, “On mathematical problems in the theory of topological insulators”, Theoret. and Math. Phys., 208:2 (2021), 1144–1155  mathnet  crossref  crossref  isi  elib
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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