Dr. Rolf Gohm - Homepage
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Address Dr. Rolf Gohm |
Research Interests
- Noncommutative Probability Theory
- Operator Algebras
- Operator Theory
- Quantum Control
EPSRC-Research Grant EP/G039275/1:
Quantum
Control: Approach based on Scattering Theory for Non-commutative Markov Chains
and Multivariate Operator Theory (2009-2012)
Summary
WIMCS Mathematical Physics Cluster Workshop (2011)
Quantum Probabilistic Symmetries
2012 LMS Midlands Regional Meeting /Workshop
QYMRU workshop (2014)
Talks
- Noncommutative independence from the infinite Braid Group and Symmetric Group (Chennai, 10th August 2010)
- Transfer Functions associated to Markov Chains (Bangalore, 14th August 2010)
- An introductory
colloquium-style talk (see the Chennai-talk above for more details)
Thoma`s theorem about extremal characters as a noncommutative de Finetti theorem (Gregynog, 23rd May 2012)
- Asymptotic Completeness for Weak Markov Processes (Sydney, 17th July 2012)
- A very introductory
10-minutes-talk for the Postgraduate Day
Repeated Interactions (Aberystwyth, 14th November 2012)
- Synchronizing Words and Preparability of States (Aberystwyth, 16th September 2013)
- Functional Models and Minimal Contractive Liftings (Amsterdam, 18th July 2014)
- Semi-Cosimplicial Objects and Spreadability (Cork, 20th August 2015)
- Braids, Cosimplicial Identities, Spreadability, Subfactors (INI Cambridge, 26th January 2017)
- A Category of Completely Positive Maps on B(H) (Chemnitz, 15th August 2017)
- Asymptotic Completeness and Controllability of Open Quantum Systems ( Paris , 11th September 2017)
- Simplicial Approach to the de Finetti Theme (Cork, 10th September 2018)
- Quantum Markov Chains (introductory 20min talk for MathsSoc, Aberystwyth, 4th March 2019)
- The probabilistic motivation to study semi-cosimplicial Hilbert spaces (UCC Mathematics Seminar, Cork, 7th January 2020)
Publications and Preprints
- Verbandstheoretische Charakterisierungen von Hilberträumen (Characterizing Hilbert space by its lattice of subspaces), Diplomarbeit, Stuttgart (1987)
- Untersuchungen über polynomiale Beschränktheit und einige spektraltheoretische Anwendungen (Polynomial boundedness and applications to spectral theory), Dissertation (PhD), Tübingen (1992)
- A spectral classification of operators related to polynomial boundedness , Journal of Operator Theory 36 (1996), 249-281
- Adapted endomorphisms which generalize Bogoljubov transformations , Journal of Operator Theory 45 (2001), 19-37
- Prediction errors and completely positive maps , in: Quantum Probability and Inf.Dim.Analysis; Proceedings Burg 2001, QP-PQ vol. XV, World Scientific (2003), 107-119
- A duality between extension and dilation , in: Advances in quantum dynamics, ed. G. Price et al., Contemp. Math. 335, Amer. Math. Soc. (2003), 139--147
- Kümmerer-Maassen scattering theory and entanglement , Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.7(2), World Scientific (2004), 271-280
- Elements of a spatial
theory for non-commutative stationary processes with discrete time index,
Habilitation Thesis (2002)
A revised version appeared as Noncommutative Stationary Processes , Lecture Notes in Mathematics 1839 , Springer-Verlag (2004) - with M.Skeide, Constructing extensions of CP-maps via tensor dilations with the help of von Neumann modules , Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.8(2), World Scientific (2005), 291-305
- with U.Franz, Random walks on finite quantum groups , Quantum Independent Increment Processes: Quantum Levy Processes, Classical Probability and Applications, Eds. U. Franz and M. Schürmann, Lecture Notes in Mathematics 1866 , Springer-Verlag (2005), 1-32
- A probabilistic index for completely positive maps and an application , Journal of Operator Theory 54(2) (2005), 339-361
- Geometric properties of the set of extensions of a stochastic matrix , Infinite Dimensional Harmonic Analysis III, Eds. H. Heyer et al., World Scientific (2005), 59-70
- with B.Kümmerer, T.Lang, Noncommutative symbolic coding , Ergodic Theory and Dynamical Systems 26 (2006), 1521-1548
- Decompositions of Beurling type for E_0-semigroups , Banach Center Publications, Vol. 73, Institute of Mathematics, Polish Academy of Sciences, Warzawa (2006), 167-176
- with S.Dey, Characteristic functions for ergodic tuples , Integral Equations and Operator Theory 58 (2007), 43-63
- with J.Gough, M.Yanagisawa Linear quantum feedback networks , Phys. Rev. A 78, 062104 (2008)
- with C.Köstler, Noncommutative independence from the braid group , Comm. Math. Phys., vol.289(2) (2009), 435-482
- Non-commutative Markov chains and multi-analytic operators , J. Math. Anal. Appl., vol.364(1) (2009), 275-288
- with S.Dey, Characteristic functions of liftings , Journal of Operator Theory 65 (2011), 17-45
- with C.Köstler, Noncommutative independence from characters of the infinite symmetric group , preprint
- with C.Köstler, Noncommutative independence in the infinite braid and symmetric group , Noncommutative harmonic analysis with applications to probability III, Banach Center Publications, Vol. 96, Institute of Mathematics, Polish Academy of Sciences, Warszawa (2012), 193-206
- Transfer Functions for Pairs of Wandering Subspaces , in: Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, Series: Operator Theory: Advances and Applications, Vol. 221, Birkhäuser (2012), 385-398.
- with S.Dey, K.J.Haria, Functional Models and Minimal Contractive Liftings , Complex Analysis and Operator Theory, Vol. 9 (4) (2015), 933-955
- with L.Bouten, J.Gough, H.Nurdin, A Trotter-Kato Theorem For Quantum Markov Limits , EPJ Quantum Technology, vol.2 (2015), EPJ Quantum Technology (2015) 2:9, 15 pages, doi:10.1140/epjqt/s40507-015-0024-2
- Weak Markov Processes as Linear Systems , Mathematics of Control, Signals, and Systems (MCSS) (2015), Math. Control Signals Syst. (2015) 27:375–413, doi:10.1007/s00498-015-0144-3
- with D.G.Evans, C.Köstler, Semi-Cosimplicial Objects and Spreadability, Rocky Mountain Journal of Mathematics, Volume 47, Number 6 (2017), 1839-1873
- with F.Haag, B.Kümmerer, Universal Preparability and Asymptotic Completeness (arXiv) ,
Communications in Mathematical Physics, 352(1) (2017), 59-94, Universal Preparability and Asymptotic Completeness (cmp), DOI 10.1007/s00220-017-2851-8 - with S.Dey, K.J.Haria, Characteristic-functions-of-liftings-II , Operators and Matrices, 12(2) (2018), 579-601, dx.doi.org/10.7153/oam-2018-12-36