Address Dr. Rolf Gohm |

- 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)

- 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)

*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