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Adam Skalski                                                                                                                                                                                                                                               Old teaching materials (mostly in Polish)
Full Professor, Deputy Director for Scientific Matters                                                                                                                                                             How I work
Institute of Mathematics
Polish Academy of Sciences

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Address: Institute of Mathematics
Polish Academy of Sciences
ul. Śniadeckich 8
00-656 Warszawa
Poland
E-mail: a.skalski at impan.pl
Page contents: Research interests
Conference plans
PhD students
Editorships
Published papers
Preprints
Various mathematical writings
A short CV
Doctoral thesis
Links
Research interests:
  • topological quantum groups, quantum symmetry groups
  • probability and harmonic analysis on quantum groups
  • topological entropy and approximation properties for C*-algebras
  • quantum stochastic processes
  • various aspects of dilation theory
  • noncommutative measure theory (ergodic limit theorems)
  • noncommutative Lp-spaces

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Conferences/meetings/research trips planned:
  • ​​​Entangling Non-commutative Functional Analysis and Geometry of Banach Spaces, Luminy, 11-15 May 2020.
  • Noncommutativity in the North, Gothenburg, 22-26 June 2020.
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    My PhD students:
    • Simeng Wang -- graduated in June 2016 (joint supervision with Quanhua Xu, Besançon)
    • Mateusz Wasilewski, graduated in June 2018
    • Haonan Zhang -- graduated in October 2019 (joint supervision with Quanhua Xu, Besançon)
    • ... place for you? (if you have a solid background in functional analysis, and a developing interest in operator algebraic techniques)

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    I am an editor of:

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    Books:
    Published papers:
    1. On the unconditional bundle convergence in L2-space over a von Neumann algebra, Probability and Mathematical Statistics, 22 (2002), pp. 19-27 (MR1944140).
    2. A few results in noncommutative ergodic theory (with V.I. Chilin and S. Litvinov), Journal of Operator Theory, 53 (2005) no.2, 331-350 (MR2153152).
    3. Quantum stochastic convolution cocycles I (with J.M. Lindsay), Annales de l`Institute Henri Poincarî, Probabilités et Statistiques, 41 (2005) no.3 (En homage a P.-A. Meyer), 581-604 (MR2139034) .
    4. On a classical scheme in noncommutative multiparameter ergodic theory, in "Quantum Probability and Infinite Dimensional Analysis," QP-PQ 18, (M. Schurmann & U. Franz, eds.), World Scientific, Singapore 2005, pp. 473-491 (available here).
    5. Quantum stochastic convolution cocycles - algebraic and C*-algebraic (with J.M. Lindsay), Banach Center Publications, 73 (2006), 313-324 (MR2423137).
    6. On quantum stochastic differential equations (with J.M. Lindsay), Journal of Mathematical Analysis and Applications, 330 (2007), no.2, 1093-1114 (available here).
    7. Completely positive quantum stochastic convolution cocycles and their dilations, Mathematical Proceedings of the Cambridge Philosophical Society, 143 (2007), 201-219 (an earlier version available here).
    8. Entropy of shifts in higher rank graph C*-algebras (with J. Zacharias), Houston Journal of Mathematics, 34 (2008), no.1, 269-282 (available here).
    9. Wold decomposition for representations of product systems of C*-correspondences (with J.Zacharias), International Journal of Mathematics, 19 (2008), no.4, 455-479 (an earlier version available here).
    10. The Banach Principle for ideal convergence in the classical and noncommutative context (with G.Horbaczewska), Journal of Mathematical Analysis and Applications, 342 (2008), no.2, 1332-1341 (an earlier version available here).
    11. Quantum stochastic convolution cocycles II (with J.M. Lindsay), Communications in Mathematical Physics, 280 (2008), no.3, 575-610 (an earlier version available here).
    12. On ergodic properties of convolution operators associated with compact quantum groups (with U.Franz), Colloquium Mathematicum, 113 (2008), no.3, 13-23 (an earlier version available here).
    13. Approximation of quantum Levy processes by quantum random walks (with U.Franz), Proceedings of the Indian Academy of Sciences. Mathematical Sciences, 118 (2008), no.2, 281-288 (available via the journal's website).
    14. Noncommutative topological entropy of endomorphisms of Cuntz algebras (with J.Zacharias), Letters in Mathematical Physics , 86 (2008), no.2, 115-134 (an earlier version available here).
    15. On spectral triples and quasidiagonality (with J.Zacharias), Expositiones Mathematicae, 27 (2009), no.2, 137-141 (available here).
    16. On idempotent states on quantum groups (with U.Franz), Journal of Algebra, 322 (2009), no.5, 1774-1802 (an earlier version available here).
    17. A new characterisation of idempotent states on finite and compact quantum groups (with U.Franz), Comptes Rendus Mathematique, 347 (2009), no.17-18, 991-996 (expanded version available here).
    18. On isometric dilations of product systems of C*-correspondences and applications to families of contractions associated to higher-rank graphs, Indiana University Mathematics Journal, 58 (2009), no.5, 2227-2252 (an earlier version available here).
    19. On approximation properties of Pimsner algebras and crossed products by Hilbert bimodules (with J.Zacharias), Rocky Mountains Journal of Mathematics, 40 (2010), no.2, 609-625 (an earlier version available here).
    20. Poisson transform on higher rank graph algebras and its applications (with J.Zacharias), Journal of Operator Theory, 63 (2010), no.2, 425-454 (an earlier version available here).
    21. Quantum isometry groups of noncommutative manifolds associated to group C*-algebras (with J.Bhowmick), Journal of Geometry and Physics, 60 (2010), no.10, 1474-1489 (an earlier version available here).
    22. Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups (with J.Zacharias), Journal of the London Mathematical Society, 82 (2010), no.1, 184-202 (an earlier version available here).
    23. Probability on topological quantum groups (in Polish), Wiadomosci Matematyczne 46 (2010), no.2, 163-196.
    24. Quantum isometry groups of 0-dimensional manifolds (with J.Bhowmick and D.Goswami), Transactions of AMS, 363 (2011), 901-921 (an earlier version available here).
    25. Convolution semigroups of states (with J.M.Lindsay), Mathematische Zeitschrift 267 (2011), 325-339 (an earlier version available here).
    26. Two-parameter families of quantum symmetry groups (with T.Banica), Journal of Functional Analysis 260 (2011), no.11, 3252-3282 (available here).
    27. On automorphisms of C*-algebras whose Voiculescu entropy is genuinely noncommutative, Ergodic Theory and Dynamical Systems 31 (2011), 951-954 (an earlier version available here).
    28. Noncommutative topological entropy of endomorphisms of Cuntz algebras II, Publications of the Research Institute of Mathematical Sciences 47 (2011), 887-896 (an earlier version available here).
    29. On Invariant MASAs for Endomorphisms of the Cuntz Algebras (with J.H.Hong and W.Szymański), Indiana University Mathematics Journal 59 (2010), no.6, 1873-1892 (an earlier version available here).
    30. A vacuum-adapted approach to quantum Feynman-Kac formulae (with A. Belton and J.M.Lindsay), Communications in Stochastic Analysis 6 (2012), no.1 (Special issue dedicated to Professor K.R.Parthasarathy), 95-109 (an earlier version available here).
    31. Quantum stochastic convolution cocycles III (with J.M.Lindsay), Mathematische Annalen 352 (2012), no.4, 779-804 (an earlier version available here).
    32. Noncommutative homogeneous spaces: the matrix case (with T. Banica and P.Sołtan), Journal of Geometry and Physics 62 (2012), no.6, 1451-1466 (an earlier version available here).
    33. Idempotent states and the inner linearity property (with T.Banica and U.Franz), Bulletin of the Polish Academy of Sciences, Mathematics 60 (2012), 123-132 (an earlier version available here).
    34. Quantum isometry groups of duals of free powers of cyclic groups (with T.Banica), International Mathematics Research Notices 9 (2012), no.6, 2094-2122 (an earlier version available here).
    35. On square roots of the Haar state on compact quantum groups (with U.Franz and R.Tomatsu), Journal of Pure and Applied Algebra 216 (2012), 2079-2093 (an earlier version available here).
    36. Closed quantum subgroups of locally compact quantum groups (with M.Daws, P. Kasprzak and P.Sołtan), Advances in Mathematics 231 (2012), 3473-3501 (an earlier version available here).
    37. Idempotent states on locally compact quantum groups (with P.Salmi), Quarterly Journal of Mathematics 63 (2012), no. 4, 1009-1032 (an earlier version available here).
    38. On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set, (with D.Goswami), Banach Center Publications 98 (2012), 199-214 (an earlier version available here).
    39. Idempotent states on the compact quantum groups and their classification on Uq(2), SUq(2), and SOq(3) (with U.Franz and R.Tomatsu), Journal of Noncommutative Geometry 7 (2013), no.1, 221-254 (an earlier version available here).
    40. Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations (with T. Banica), Proceedings of the London Mathematical Society 106 (2013), no.5, 980-1004 (an earlier version available here).
    41. Quantum random walk approximation on locally compact quantum groups (with J.M.Lindsay), Letters in Mathematical Physics 103 (2013), no.7, 765-775 (an earlier version available here).
    42. Inclusions of ternary rings of operators and conditional expectations (with P.Salmi), Mathematical Proceedings of the Cambridge Philosophical Society, 155 (2013), no.3, 475-482 (an earlier version available here).
    43. On spectral triples on crossed products arising from equicontinuous actions (with A.Hawkins, S.White and J.Zacharias), Mathematica Scandinavica, 113 (2013), no.2, 262-291 (an earlier version available here).
    44. Quantum Feynman-Kac perturbations (with A. Belton and J.M.Lindsay), Journal of the London Mathematical Society 89 (2014) no.1, 275-300 (an earlier version available here).
    45. Contractive idempotents on locally compact quantum groups (with M.Neufang, P.Salmi and N.Spronk), Indiana University Mathematics Journal 62 (2013), no.6, 1983-2002 (an earlier version available here).
    46. Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras (with M.Caspers, R.Okayasu and R.Tomatsu), Comptes Rendus Mathematique 252 (2014), 507-510 (an earlier version available here).
    47. Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras (with P.Sołtan), Infinite Dimensional Analysis, Quantum Probability and Related Topics 17 (2014), no.2, 1450012, 27 pages (an earlier version available here).
    48. Quantum group of automorphisms of a finite quantum group (with J.Bhowmick and P.Sołtan), Journal of Algebra 423 (2015), 514-537, an earlier version available here.
    49. The quantum algebra of partial Hadamard matrices (with T.Banica), Linear Algebra and its Applications 469 (2015), 364-380, an earlier version available here.
    50. The Haagerup property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms (with M.Caspers), Communications in Mathematical Physics 336 (2015), no.3, 1637-1664, an earlier version available here.
    51. One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry (with B.Das, U.Franz and A.Kula), Mathematische Zeitschrift 281 (2015), no.3-4, 949-965, an earlier version available here.
    52. The Haagerup property for arbitrary von Neumann algebras (with M.Caspers), International Mathematics Research Notices 19 (2015), no.6, 9857-9887 (an earlier version available here).
    53. The Haagerup property for locally compact quantum groups (with M.Daws, P.Fima and S.White), Journal fur die Reine und Angewandte Mathematik 711 (2016), 189-229, an earlier version available here.
    54. Quantum families of invertible maps and related problems (with P.Sołtan), Canadian Journal of Mathematics 68 (2016), no.3, 698-720, an earlier version available here.
    55. Lévy Processes on Quantum Permutation Groups (with U.Franz and A.Kula), Operator Theory: Advances and Applications 252 (2016), no.3, 193-259 (an earlier version available here).
    56. Open quantum subgroups of locally compact quantum groups (with M.Kalantar and P.Kasprzak), Advances in Mathematics 303 (2016), no.3, 322-359 (an earlier version available here).
    57. Integration over the quantum diagonal subgroup and associated Fourier-like algebras (with U.Franz and H.H.Lee), International Journal of Mathematics 27 (2016), no.9, 1650073, 37 pp. (an earlier version available here).
    58. Introduction to compact and discrete quantum groups (with U.Franz and P.Sołtan), Banach Center Publications 111 (2017), 9-31 (an earlier version available here).
    59. Around Property (T) for quantum groups (with M.Daws and A.Viselter), Communications in Mathematical Physics 353 (2017), no.1, 69–118 (an earlier version available here).
    60. The canonical central exact sequence for locally compact quantum groups (with P.Kasprzak and P.Sołtan), Mathematische Nachrichten 290 (2017), no.8-9, 1303-1316 (an earlier version available here).
    61. Idempotent states on locally compact quantum groups II (with P.Salmi), Quarterly Journal of Mathematics 68 (2017), no.2, 421-431 (an earlier version available here).
    62. Actions of locally compact (quantum) groups on ternary rings of operators, their crossed products and generalized Poisson boundaries (with P.Salmi), Kyoto Journal of Mathematics 57 (2017), no.3, 667-691 (an earlier version available here).
    63. Wreath products of finite groups by quantum groups (with A.Freslon), Journal of Noncommutative Geometry 12 (2018), no.1, 29-68 (an earlier version available here).
    64. Remarks on factoriality and q-deformations (with S.Wang), Proceedings of the AMS 146 (2018), no.9, 3813-3823 (an earlier version available here).
    65. Quantum actions on discrete quantum spaces and a generalization of Clifford's theory of representations (with K.De Commer, P.Kasprzak and P.Sołtan), Israel Journal of Mathematics 226 (2018), no.1, 475-503 (an earlier version available here).
    66. Lévy-Khintchine decompositions for generating functionals on universal CQG-algebras (with B.Das, U.Franz and A.Kula), IDAQP 21 (2018), no.3, 1850017, 36 pages, (an earlier version available here).
    67. Positive Herz-Schur multipliers and approximation properties of crossed products (with Andrew McKee, Ivan Todorov and Lyudmila Turowska) Mathematical Proceedings of the Cambridge Philosophical Society 165 (2018), no.3, 511-532 (an earlier version available here).
    68. Convolution semigroups on locally compact quantum groups and noncommutative Dirichlet forms (with A.Viselter), Journal de Mathématiques Pures et Appliquées 124 (2019), 59-105 (an earlier version available here).
    69. Quantum symmetries of the twisted tensor products of C*-algebras (with J.Bhowmick, A.Mandal and S.Roy), Communications in Mathematical Physics 368 (2019), no.3, 1051-1085 (an earlier version available here).
    70. On C*-completions of discrete quantum group rings (with M.Caspers), to appear in Bulletin of the London Mathematical Society 51 (2019), no.4, 691-704 (an earlier version available here).
    71. On MASAs in q-deformed von Neumann algebras (with M.Caspers and M.Wasilewski), Pacific Journal of Mathematics 302 (2019), no.1, 1-21(an earlier version available here).

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    Preprints:
    1. Induction for locally compact quantum groups revisited (with M.Kalantar, P.Kasprzak and P.Sołtan, 20 pp.), to appear in Proceedings of the Royal Society of Edinburgh Section A (an earlier version available here).
    2. Generating functionals for locally compact quantum groups (with A.Viselter, 24 pp.), available here.
    3. Maximal subgroups and von Neumann subalgebras with the Haagerup property (with Y.Jiang, 29 pp.), available here.
    4. Fixed points and limits of convolution powers of contractive quantum measures (with M.Neufang, P.Salmi and N.Spronk, 26 pp.), available here.

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    Various writings:

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    A short CV: Born: 31.01.1978
    Degrees:
    2000 MSc in Mathematics, University of Łódź
    2002 MSc in Physics, University of Łódź
    2006 PhD in Mathematics, University of Nottingham
    2013 Habilitation in Mathematics, Mathematical Institute of the Polish Academy of Sciences
    2019 Professor of Mathematics
    Previous positions:
    2000-2004 Assistant Pre-Doc, Department of Mathematics, University of Łódź
    2004-2005 PhD student, University of Nottingham
    I-VII 2006 Research Associate, Lancaster University
    VIII 2006 - VII 2007 EPSRC Research Fellow, University of Nottingham
    X-XI 2009 Short Term JSPS Postdoctoral Fellow, Tokyo University
    VIII 2007 - IX 2010 EPSRC Post-Doctoral Fellow, Lancaster University
    X 2010 - IX 2012 Intra-European Marie Curie Fellow, Mathematical Institute of the Polish Academy of Sciences, Warsaw
    X 2012 - IX 2015 Assistant Professor, joint position at the Mathematical Institute of the Polish Academy of Sciences and University of Warsaw
    X 2014 - XII 2014 Professeur Invité CNRS, Université Franche-Comté, Besançon
    Full CV

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    Doctoral thesis: My thesis, `Quantum stochastic convolution cocycles', was concerned with a generalisation of the theory of quantum Lévy processes on algebraic *-bialgebras to the context of compact quantum groups, or, more generally, C*-bialgebras. It was written under supervision of Martin Lindsay, submitted to the University of Nottingham in December 2005 and defended on the 28th July 2006.

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    Links: My (current) collaborators (who happen to have websites):
    Teodor Banica
    Alex Belton
    Martijn Caspers
    Matt Daws
    Pierre Fima
    Uwe Franz
    Amaury Freslon
    Yongle Jiang
    Mehrdad Kalantar
    Paweł Kasprzak
    Martin Lindsay
    Sutanu Roy
    Pekka Salmi
    Piotr Sołtan
    Nico Spronk
    Ivan Todorov
    Reiji Tomatsu
    Ami Viselter
    Stuart White
    Joachim Zacharias

    Institutions I am/have been related to:
    Department of Mathematics, University of Łódź
    School of Mathematical Sciences, University of Nottingham
    Department of Mathematics and Statistics, Lancaster University
    Mathematical Institute of the Polish Academy of Sciences (Warsaw)
    Faculty of Mathematics, Informatics and Mechanics, University of Warsaw
    Département de mathématiques Université Franche-Comté, Besançon

    Daily tools and readings:
    Mathscinet
    Arxiv

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    Last updated by: ® Adam Skalski 2019-11-10