A categorial-algebraic description of $K$-theory for $C^*$-algeras was obtained. In a series of joint papers with K. Thomsen coincidence of $E$-theory of Connes–Higson with the functor of $C^*$-algebra extensions was proved. Relations between almost, asymptotic and Fredholm representations of discrete groups were studied. Diagonalization theorem for compact operators on Hilbert $C^*$-modules was proved for a wide class of $C^*$-algebras.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1983 (department of higher geometry and topology). Ph.D. thesis was defended in 1987. D.Sci. thesis was defended in 2000. A list of my works contains more than 50 titles. Since 1996 I jointly with A. S. Mishchenko and E. V. Troitsky have led the research seminar at MSU on non-commutative topology.
Main publications:
Manuilov V. M. Diagonalization of compact operators in Hilbert modules over finite $W^*$-algebras // Annals of Global Anal. and Geom. 1995, 13(3), 207–226.
Manuilov V. M., Thomsen K. Quasidiagonal extensions and sequentially trivial asymptotic homomorphisms // Adv. Math. (2000), 154, 258–279.
V. M. Manuilov, “Hilbert $C^*$-modules related to discrete metric spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 5, 55–63; Russian Math. (Iz. VUZ), 65:5 (2021), 40–47
2018
2.
V. M. Manuilov, “Symmetrization of Cuntz' Picture for the Kasparov $KK$-Bifunctor”, Funktsional. Anal. i Prilozhen., 52:3 (2018), 32–41; Funct. Anal. Appl., 52:3 (2018), 186–193
V. M. Manuilov, “Pairs of operators with equal defect from unitarity and their relative index”, Mat. Sb., 208:10 (2017), 113–125; Sb. Math., 208:10 (2017), 1523–1534
2008
4.
V. M. Manuilov, Yu. Chao, “On Almost Representations of Groups with Property (T)”, Mat. Zametki, 84:2 (2008), 219–230; Math. Notes, 84:2 (2008), 207–217
V. M. Manuilov, K. Thomsen, “Translation Invariant Asymptotic Homomorphisms and Extensions of $C^*$-Algebras”, Funktsional. Anal. i Prilozhen., 39:3 (2005), 87–91; Funct. Anal. Appl., 39:3 (2005), 236–239
V. M. Manuilov, K. Thomsen, “The Connes–Higson map is an isomorphism”, Uspekhi Mat. Nauk, 56:4(340) (2001), 151–152; Russian Math. Surveys, 56:4 (2001), 756–757
V. M. Manuilov, K. Thomsen, “Asymptotically split extensions and $E$-theory”, Algebra i Analiz, 12:5 (2000), 142–157; St. Petersburg Math. J., 12:5 (2001), 819–830
V. M. Manuilov, “On Almost Representations of Groups $\pi\times{\mathbf Z}$”, Trudy Mat. Inst. Steklova, 225 (1999), 257–263; Proc. Steklov Inst. Math., 225 (1999), 243–249
V. M. Manuilov, “An Invariant of a Pair of Almost Commuting Unbounded Operators”, Funktsional. Anal. i Prilozhen., 32:4 (1998), 88–91; Funct. Anal. Appl., 32:4 (1998), 288–291
V. M. Manuilov, A. S. Mishchenko, “Asymptotic and Fredholm representations of discrete groups”, Mat. Sb., 189:10 (1998), 53–74; Sb. Math., 189:10 (1998), 1485–1504
V. M. Manuilov, E. V. Troitskii, M. Frank, “Actions of groups and conditional expectations of finite index”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, no. 2, 30–34
1997
16.
V. M. Manuilov, “On Almost Commuting Operators”, Funktsional. Anal. i Prilozhen., 31:3 (1997), 80–82; Funct. Anal. Appl., 31:3 (1997), 212–213
V. M. Manuilov, “Diagonalization of compact operators on Hilbert modules over $C^*$-algebras of real rank zero”, Mat. Zametki, 62:6 (1997), 865–870; Math. Notes, 62:6 (1997), 726–730
V. M. Manuilov, “Spectrally stable relations”, Uspekhi Mat. Nauk, 52:2(314) (1997), 175–176; Russian Math. Surveys, 52:2 (1997), 412–413
19.
V. M. Manuilov, “Diagonalization of operators over continuous fields of $C^*$-algebras”, Mat. Sb., 188:6 (1997), 99–118; Sb. Math., 188:6 (1997), 893–911
V. M. Manuilov, “Local minima of commutator norms in finite factors”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1997, no. 3, 25–28
1996
21.
V. M. Manuilov, “Representability of Functionals on Hilbert $C^*$-Modules”, Funktsional. Anal. i Prilozhen., 30:4 (1996), 83–86; Funct. Anal. Appl., 30:4 (1996), 287–289
V. M. Manuilov, “On the Eigenvalues of the Perturbed Schrödinger Operator with Irrational Magnetic Flow”, Funktsional. Anal. i Prilozhen., 28:2 (1994), 57–60; Funct. Anal. Appl., 28:2 (1994), 120–122
23.
V. M. Manuilov, “Diagonalization of compact operators in Hilbert modules over finite $W^*$-algebras”, Uspekhi Mat. Nauk, 49:2(296) (1994), 159–160; Russian Math. Surveys, 49:2 (1994), 166–167
V. M. Manuilov, “On the group $K_0$ of a continuous family of algebras $A_\theta$”, Uspekhi Mat. Nauk, 44:3(267) (1989), 163–164; Russian Math. Surveys, 44:3 (1989), 206–207
V. M. Manuilov, “Algebraic duality between homology and cohomology”, Uspekhi Mat. Nauk, 41:3(249) (1986), 165–166; Russian Math. Surveys, 41:3 (1986), 221–222
27.
V. M. Manuilov, “$K$-homology of $C^*$-algebras”, Mat. Sb. (N.S.), 131(173):4(12) (1986), 536–543; Math. USSR-Sb., 59:2 (1988), 533–540
2001
28.
A. A. Irmatov, O. B. Lupanov, V. P. Maslov, V. M. Manuilov, A. A. Mikhalev, V. A. Sadovnichii, Yu. P. Solov'ev, E. V. Troitskii, A. T. Fomenko, “Aleksandr Sergeevitch Mischenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, no. 5, 67–69
Дискретизации пространств и алгебры Роу V. M. Manuilov International conference
“Theory of Functions, Operator Theory and Quantum Information Theory” June 11, 2024 12:50
О тривиальности препятствия к существованию проектора Ваннье V. M. Manuilov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) March 13, 2024 18:30
Bill Paschke (1946-2019) V. M. Manuilov International Workshop "Hilbert $C^*$-Modules Online Weekend"
in memory of William L. Paschke (1946–2019) December 5, 2020 08:00
K-theory and balanced pairs V. M. Manuilov General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences November 17, 2016 14:00
27.
Extensions of C*-algebras V. M. Manuilov St. Petersburg Seminar on Representation Theory and Dynamical Systems November 16, 2016 17:00
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