Rozmiar: 71802 bajtów

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

back to top

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

back to top

Conferences/meetings/research trips planned:

back to top

My PhD students:
  • Simeng Wang -- graduated in June 2016 (joint supervision with Quanhua Xu, Besançon)
  • Mateusz Wasilewski, graduation planned in 2017/2018

back to top

I am an editor of:

back to top

Book: "Noncommutative Mathematics for Quantum Systems" (with Uwe Franz), Cambridge IISc Series, 2015.
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.

back to top

Preprints:
  1. Lévy Processes on Quantum Permutation Groups (with U.Franz and A.Kula, 60 pp.), to appear in Proceedings of the Conference `Noncommutative Analysis, Operator Theory, and Applications', Milano, 2014, Birkhauser (an earlier version available here).
  2. Wreath products of finite groups by quantum groups (with A.Freslon, 25 pp.), to appear in Journal of Noncommutative Geometry (an earlier version available here).
  3. Actions of locally compact (quantum) groups on ternary rings of operators, their crossed products and generalized Poisson boundaries (with P.Salmi, 19 pp.), to appear in Kyoto Journal of Mathematics (an earlier version available here).
  4. Integration over the quantum diagonal subgroup and associated Fourier-like algebras (with U.Franz and H.H.Lee, 31 pp.), to appear in International Journal of Mathematics , (an earlier version available here).
  5. Short exact sequence e -> Z(G) -> G -> Inn(G) -> e for locally compact quantum groups (with P.Kasprzak and P.Sołtan, 20 pp.), available here.
  6. Open quantum subgroups of locally compact quantum groups (with M.Kalantar and P.Kasprzak, 30 pp.), available here.
  7. Around Property (T) for quantum groups (with M.Daws and A.Viselter, 49 pp.), available here.
  8. Idempotent states on locally compact quantum groups II (with P.Salmi, 9 pp), available here.
  9. Remarks on factoriality and q-deformations (with S.Wang, 9 pp), available here.

back to top

Various writings:

back to top

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
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

back to top

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.

back to top

Links: My (current) collaborators (who happen to have websites):
Teodor Banica
Alex Belton
Martijn Caspers
Matt Daws
Pierre Fima
Uwe Franz
Amaury Freslon
Mehrdad Kalantar
Paweł Kasprzak
Martin Lindsay
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

back to top

Last updated by: ® Adam Skalski 2016-07-20