Quantum Control: Approach based on Scattering Theory for Non-commutative Markov Chains and Multivariate Operator Theory
Lead Research Organisation:
Aberystwyth University
Department Name: Inst of Mathematical and Physical Sci
Abstract
Modern control theory has frequently used concepts and results from abstract mathematics. The aim of this proposal is to explore genuinely non-commutativeversions with a view toward direct applications to the emergent discipline of quantum control. Some elements of open-loop and closed-loop control have already been developed, and recently there has been much interest in fully quantum (or, coherent) control models. Experimental advances mean that physicists have anunprecedented ability to manipulate quantum mechanical systems, and from the technological point of view there is currently much interest in deriving atheory of quantum engineering as the foundation for a much anticipated quantum technological revolution.The proposed research is on the theoretical side and aims to enlarge the toolkit of mathematical methods available to control quantum systems. The classical theory of control has many deep and productive connections with disciplines of mathematical analysis. Complex analysis is indispensable in the use of Laplace transforms and transfer functions for controlled systems. Based on that the theory of state space models and robust control profited from ideas in operator theory. But there are difficulties to adapt these methods to the world of noncommutative mathematics needed for quantum control. There is partial success in specific models but an integrated, first-principles discipline of quantum control is still missing.A basic idea of this proposal is to make use of recent developments in multivariate operator theory. While in classical operator theory a single operator is analysed, in multivariate operator theory the joint action of a family of operators is studied. These operators may not commute with each other. Nevertheless there are analogues to classical results in complex analysis such as the idea of multi-analytic operators. In fact, many of the operator results which are relevant for classical control theory can be extended to this setting. We propose to develop these tools with applications to quantum control. Scattering theory for non-commutative Markov chains is a theory about open quantum systems with many connections to operator theory. Recently the wave operator occurring in this theory has been rewritten as a multi-analytic operator. On the other hand it is possible to interpret this theory as a version of open-loop control, for example it has been successfully applied to the preparation of states in a micromaser interacting with a stream of atoms. Hence it is very natural to start here to develop the methods of multivariate operator theory as applied to the problems in quantum control.Once the bridge between quantum control and multivariate operator theory is understood in the specific directions described above we speculate that a considerable amount of related and deep mathematics becomes available for engineering applications. In the later parts of the project this also includes the more advanced methods of robust control.The investigators Dr Gohm and Professor Gough are the members of the Quantum Control Research Group at Aberystwyth University, set up in 2007. Both have a strong background in mathematical physics and they share the conviction that building bridges between the demands of an applied discipline such as quantum control and ideas in pure mathematics such as multivariate operator theory is as interesting as it is useful.
Organisations
People |
ORCID iD |
Rolf Gohm (Principal Investigator) | |
John Gough (Co-Investigator) |
Publications
Gough J
(2010)
Quantum filtering for systems driven by fermion fields
Gough J
(2012)
Quantum filtering for systems driven by fields in single photon states and superposition of coherent states using non-Markovian embeddings
in Quantum Information Processing
Gough J
(2010)
Quantum filtering in coherent states
in Communications on Stochastic Analysis
Gough J
(2010)
Squeezing components in linear quantum feedback networks
in Physical Review A
Gohm R
(2017)
Universal Preparability of States and Asymptotic Completeness
in Communications in Mathematical Physics
Gohm R
(2015)
Weak Markov processes as linear systems
in Mathematics of Control, Signals, and Systems
Description | There has been substantial progress in the original program to develop the links between some pure mathematics in operator theory and applications to quantum stochastic processes, quantum control and concrete quantum physical systems. The cooperation with researchers from India, in particular with Prof. S. Dey from IIT Mumbai, is ongoing. We see recent progress in pure mathematics inspired by this research in [Santanu Dey, Rolf Gohm, Kalpesh J. Haria: Functional Models and Minimal Contractive Liftings, published in: Complex Analysis and Operator Theory]. There was an unexpected development resulting in work on noncommutative independence in braid and symmetric groups by R. Gohm and C. Koestler during the grant period. This inspired new connections between quantum stochastic processes and algebra and there was a session in the George Boole Conference in Cork (August 2015) where we reported on recent developments. It was justified to spend part of our time on these exciting new ideas. Research on this topic is also ongoing. |
Exploitation Route | My colleagues and I put considerable effort to feed our research results into the relevant research communities, see also: Further Funding. In particular I want to mention that I explained this research at the annual IWOTA conferences where I found a lot of interest by operator theorists. |
Sectors | Digital/Communication/Information Technologies (including Software),Other |
URL | http://users.aber.ac.uk/rog/ |
Description | "Institute of Mathematical Sciences, Chen" |
Amount | £700 (GBP) |
Funding ID | Conference Participation of Claus Koestler |
Organisation | Institute of Mathematical Sciences, Chennai |
Sector | Academic/University |
Country | India |
Start | 08/2010 |
End | 08/2010 |
Description | "Institute of Mathematical Sciences, Chen" |
Amount | £700 (GBP) |
Funding ID | Conference Participation of Claus Koestler |
Organisation | Institute of Mathematical Sciences, Chennai |
Sector | Academic/University |
Country | India |
Start | 08/2010 |
End | 08/2010 |
Description | Aberystwyth University |
Amount | £150 (GBP) |
Funding ID | Research Visit of Benoit Collins |
Organisation | Aberystwyth University |
Sector | Academic/University |
Country | United Kingdom |
Start | 09/2012 |
End | 10/2012 |
Description | Aberystwyth University |
Amount | £150 (GBP) |
Funding ID | Research Visit of Benoit Collins |
Organisation | Aberystwyth University |
Sector | Academic/University |
Country | United Kingdom |
Start | 09/2012 |
End | 10/2012 |
Description | Cardiff University |
Amount | £500 (GBP) |
Funding ID | Participation at Meeting of Claus Koestler |
Organisation | Cardiff University |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2011 |
End | 04/2011 |
Description | Cardiff University |
Amount | £400 (GBP) |
Funding ID | Participation at EU-NCG Meeting of Claus Koestler |
Organisation | Cardiff University |
Sector | Academic/University |
Country | United Kingdom |
Start | 02/2010 |
End | 03/2010 |
Description | Cardiff University |
Amount | £500 (GBP) |
Funding ID | Participation at Meeting of Claus Koestler |
Organisation | Cardiff University |
Sector | Academic/University |
Country | United Kingdom |
Start | 02/2011 |
End | 03/2011 |
Description | Cardiff University |
Amount | £400 (GBP) |
Funding ID | Participation at EU-NCG Meeting of Claus Koestler |
Organisation | Cardiff University |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2010 |
End | 04/2010 |
Description | EU-NCG Network in Noncommutative Geometr |
Amount | £1,000 (GBP) |
Funding ID | EU-NC - UKIERI - WIMCS Mathematical Physics Cluster Wor |
Organisation | Network in Noncommutative Geometry (EU-NCG) |
Sector | Academic/University |
Country | European Union (EU) |
Start | 05/2011 |
End | 05/2011 |
Description | EU-NCG Network in Noncommutative Geometry |
Amount | £1,000 (GBP) |
Funding ID | EU-NC - UKIERI - WIMCS Mathematical Physics Cluster Workshop |
Organisation | Network in Noncommutative Geometry (EU-NCG) |
Sector | Academic/University |
Country | European Union (EU) |
Start | 02/2011 |
End | 03/2011 |
Description | Franche Comte University |
Amount | £700 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Franche-Comté |
Sector | Academic/University |
Country | France |
Start | 01/2010 |
Description | Franche Comte University |
Amount | £700 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Franche-Comté |
Sector | Academic/University |
Country | France |
Start | 04/2010 |
End | 04/2010 |
Description | Georg-August University Goettingen |
Amount | £600 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Göttingen |
Sector | Academic/University |
Country | Germany |
Start | 04/2011 |
End | 05/2011 |
Description | Georg-August University Goettingen |
Amount | £600 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Göttingen |
Sector | Academic/University |
Country | Germany |
Start | 07/2011 |
End | 08/2011 |
Description | Indian Institute of Technology |
Amount | £500 (GBP) |
Funding ID | Research Visit of Rolf Gohm |
Organisation | Indian Institutes of Technology |
Sector | Academic/University |
Country | India |
Start | 07/2010 |
End | 08/2010 |
Description | Indian Institute of Technology |
Amount | £500 (GBP) |
Funding ID | Research Visit of Rolf Gohm |
Organisation | Indian Institutes of Technology |
Sector | Academic/University |
Country | India |
Start | 07/2010 |
End | 08/2010 |
Description | Institute of Mathematical Sciences Chenn |
Amount | £700 (GBP) |
Funding ID | Conference Participation of Rolf Gohm |
Organisation | Institute of Mathematical Sciences |
Sector | Academic/University |
Country | India |
Start | 07/2010 |
End | 08/2010 |
Description | Institute of Mathematical Sciences Chenn |
Amount | £700 (GBP) |
Funding ID | Conference Participation of Rolf Gohm |
Organisation | Institute of Mathematical Sciences, Chennai |
Sector | Academic/University |
Country | India |
Start | 08/2010 |
End | 08/2010 |
Description | Institute of Physics |
Amount | £250 (GBP) |
Funding ID | Midlands Regional Meeting & Workshop |
Organisation | Institute of Physics (IOP) |
Sector | Learned Society |
Country | United Kingdom |
Start | 08/2012 |
End | 09/2012 |
Description | Kyoto University |
Amount | £4,900 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Kyoto |
Sector | Academic/University |
Country | Japan |
Start | 11/2011 |
End | 12/2011 |
Description | Kyoto University |
Amount | £4,900 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Kyoto |
Sector | Academic/University |
Country | Japan |
Start | 11/2011 |
End | 12/2011 |
Description | London Mathematical Society |
Amount | £7,500 (GBP) |
Funding ID | Midlands Regional Meeting & Workshop |
Organisation | London Mathematical Society |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2012 |
End | 09/2012 |
Description | London Mathematical Society |
Amount | £7,500 (GBP) |
Funding ID | Midlands Regional Meeting & Workshop |
Organisation | London Mathematical Society |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2012 |
End | 09/2012 |
Description | Loughborough University |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Loughborough University |
Sector | Academic/University |
Country | United Kingdom |
Start | 05/2011 |
End | 06/2011 |
Description | Memorial University of Newfoundland |
Amount | £1,500 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Memorial University of Newfoundland |
Sector | Academic/University |
Country | Canada |
Start | 11/2010 |
End | 11/2010 |
Description | Memorial University of Newfoundland |
Amount | £1,500 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Memorial University of Newfoundland |
Sector | Academic/University |
Country | Canada |
Start | 01/2010 |
Description | Newcastle University |
Amount | £150 (GBP) |
Funding ID | Research Visit of Rolf Gohm |
Organisation | Newcastle University |
Sector | Academic/University |
Country | United Kingdom |
Start | 09/2009 |
End | 10/2009 |
Description | Queen's University Canada |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Queen's University |
Sector | Academic/University |
Country | Canada |
Start | 06/2010 |
End | 08/2010 |
Description | Queen's University Canada |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Queen's University |
Sector | Academic/University |
Country | Canada |
Start | 06/2010 |
Description | Saarland University |
Amount | £400 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Saarland University |
Sector | Academic/University |
Country | Germany |
Start | 05/2012 |
End | 06/2012 |
Description | Saarland University |
Amount | £400 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Saarland University |
Sector | Academic/University |
Country | Germany |
Start | 04/2012 |
End | 05/2012 |
Description | Saskatoon Research Center |
Amount | £1,600 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Saskatoon Research Center |
Sector | Private |
Country | Canada |
Start | 01/2010 |
Description | Saskatoon Research Center |
Amount | £1,600 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Saskatoon Research Center |
Sector | Private |
Country | Canada |
Start | 03/2010 |
End | 03/2010 |
Description | Swiss Federal Institute of Technology (ETH), Zurich |
Amount | £250 (GBP) |
Funding ID | Invited Research Visit of Claus Koestler |
Organisation | ETH Zurich |
Sector | Academic/University |
Country | Switzerland |
Start | 03/2012 |
End | 04/2012 |
Description | Swiss Federal Institute of Technology (ETH), Zurich |
Amount | £250 (GBP) |
Organisation | ETH Zurich |
Sector | Academic/University |
Country | Switzerland |
Start | 01/2012 |
Description | Swiss Federal Institute of Technology (ETH), Zurich |
Amount | £250 (GBP) |
Organisation | ETH Zurich |
Sector | Academic/University |
Country | Switzerland |
Start | 01/2012 |
Description | The Erwin-Schroedinger Institute |
Amount | £800 (GBP) |
Funding ID | Workshop Participation of Claus Koestler |
Organisation | University of Vienna |
Department | Erwin Schroedinger Institute for Mathematical Physics |
Sector | Academic/University |
Country | Austria |
Start | 01/2011 |
Description | The Erwin-Schroedinger Institute |
Amount | £1,200 (GBP) |
Funding ID | Workshop Participation of Claus Koestler |
Organisation | University of Vienna |
Department | Erwin Schroedinger Institute for Mathematical Physics |
Sector | Academic/University |
Country | Austria |
Start | 06/2011 |
End | 09/2011 |
Description | The Erwin-Schroedinger Institute |
Amount | £800 (GBP) |
Funding ID | Workshop Participation of Claus Koestler |
Organisation | University of Vienna |
Department | Erwin Schroedinger Institute for Mathematical Physics |
Sector | Academic/University |
Country | Austria |
Start | 02/2011 |
End | 02/2011 |
Description | The Erwin-Schroedinger Institute |
Amount | £1,200 (GBP) |
Funding ID | Workshop Participation of Claus Koestler |
Organisation | University of Vienna |
Department | Erwin Schroedinger Institute for Mathematical Physics |
Sector | Academic/University |
Country | Austria |
Start | 04/2011 |
End | 04/2011 |
Description | Tohoku University (Japan) |
Amount | £4,200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Tohoku University |
Sector | Academic/University |
Country | Japan |
Start | 10/2010 |
End | 12/2010 |
Description | Tohoku University (Japan) |
Amount | £4,200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | Tohoku University |
Sector | Academic/University |
Country | Japan |
Start | 10/2010 |
End | 12/2010 |
Description | Trinity College Dublin |
Amount | £250 (GBP) |
Funding ID | Research Visit of Rolf Gohm |
Organisation | Trinity College Dublin |
Sector | Academic/University |
Country | Ireland |
Start | 03/2011 |
End | 04/2011 |
Description | UK India Education & Research Initiative |
Amount | £500 (GBP) |
Funding ID | Participation at Conference of Claus Koestler |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2012 |
End | 04/2012 |
Description | UK India Education & Research Initiative |
Amount | £1,500 (GBP) |
Funding ID | Conference Participation of Rolf Gohm |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2010 |
End | 09/2010 |
Description | UK India Education & Research Initiative |
Amount | £1,000 (GBP) |
Funding ID | EU-NC - UKIERI - WIMCS Mathematical Physics Cluster Workshop |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2011 |
Description | UK India Education & Research Initiative |
Amount | £500 (GBP) |
Funding ID | Participation at Conference of Rolf Gohm |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2012 |
End | 04/2012 |
Description | UK India Education & Research Initiative |
Amount | £1,500 (GBP) |
Funding ID | Conference Participation of Claus Koestler |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2010 |
End | 09/2010 |
Description | UK India Education & Research Initiative |
Amount | £1,100 (GBP) |
Funding ID | Conference Participation of Claus Koestler |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 09/2011 |
End | 10/2011 |
Description | UK India Education & Research Initiative |
Amount | £1,500 (GBP) |
Funding ID | Conference Participation of Rolf Gohm |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2010 |
End | 09/2010 |
Description | UK India Education & Research Initiative |
Amount | £1,100 (GBP) |
Funding ID | Conference Participation of Claus Koestler |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2011 |
End | 09/2011 |
Description | UK India Education & Research Initiative |
Amount | £1,500 (GBP) |
Funding ID | Conference Participation of Claus Koestler |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2010 |
End | 10/2010 |
Description | UK India Education & Research Initiative |
Amount | £1,000 (GBP) |
Funding ID | EU-NC - UKIERI - WIMCS Mathematical Physics Cluster Workshop |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2011 |
End | 04/2011 |
Description | UK India Education & Research Initiative |
Amount | £500 (GBP) |
Funding ID | Participation at Conference of Rolf Gohm |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2012 |
End | 09/2012 |
Description | UK India Education & Research Initiative |
Amount | £500 (GBP) |
Funding ID | Participation at Conference of John Gough |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2012 |
End | 09/2012 |
Description | UK India Education & Research Initiative |
Amount | £500 (GBP) |
Funding ID | Participation at Conference of John Gough |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2012 |
End | 04/2012 |
Description | UK India Education & Research Initiative |
Amount | £500 (GBP) |
Funding ID | Participation at Conference of Claus Koestler |
Organisation | UK-India Education and Research Initiative (UKIERI) |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2012 |
Description | University of Aberdeen |
Amount | £600 (GBP) |
Funding ID | Invited Research Visit of Claus Koestler |
Organisation | University of Aberdeen |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2012 |
End | 09/2012 |
Description | University of Molise |
Amount | £700 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Molise |
Sector | Academic/University |
Country | Italy |
Start | 03/2010 |
End | 03/2010 |
Description | University of Molise |
Amount | £700 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Molise |
Sector | Academic/University |
Country | Italy |
Start | 01/2010 |
Description | University of Newcastle Australia |
Amount | £2,500 (GBP) |
Funding ID | Invited Research Visit of Claus Koestler |
Organisation | Newcastle University |
Sector | Academic/University |
Country | United Kingdom |
Start | 04/2012 |
End | 04/2012 |
Description | University of Newcastle Australia |
Amount | £2,500 (GBP) |
Funding ID | Invited Research Visit of Claus Koestler |
Organisation | University of Newcastle |
Sector | Academic/University |
Country | Australia |
Start | 08/2012 |
End | 09/2012 |
Description | University of Nottingham |
Amount | £200 (GBP) |
Funding ID | Research visit of Claus Koestler |
Organisation | University of Nottingham |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2010 |
Description | University of Nottingham |
Amount | £150 (GBP) |
Funding ID | Research Visit of Rolf Gohm |
Organisation | University of Nottingham |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2011 |
End | 04/2011 |
Description | University of Ottawa |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Ottawa |
Sector | Academic/University |
Country | Canada |
Start | 06/2010 |
End | 07/2010 |
Description | University of Ottawa |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Ottawa |
Sector | Academic/University |
Country | Canada |
Start | 01/2010 |
Description | University of Oxford |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler |
Organisation | University of Oxford |
Sector | Academic/University |
Country | United Kingdom |
Start | 04/2010 |
End | 05/2010 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Participation at Meeting of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 12/2009 |
End | 12/2009 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Invited Colloquium Participation of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £3,000 (GBP) |
Funding ID | Midlands Regional Meeting & Workshop |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 09/2012 |
End | 09/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Workshop participation of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 02/2010 |
End | 02/2010 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Invited Colloquium Participation of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 05/2012 |
End | 05/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Participation at Meeting of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2011 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Workshop participation of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2010 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Participation at Meeting of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2011 |
End | 03/2011 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | nvited Colloquium Participation of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 05/2012 |
End | 05/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | nvited Colloquium Participation of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Invited Participation at Meeting of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 04/2012 |
End | 04/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Invited Participation at Meeting of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Presentation of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2010 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Participation at Meeting of Rolf Gohm |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2011 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler at University of Cardi |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 12/2009 |
End | 12/2009 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £1,000 (GBP) |
Funding ID | EU-NC- UKIERI - WIMCS Mathematical Physics Cluster Work |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2011 |
End | 02/2011 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £3,000 (GBP) |
Funding ID | Midlands Regional Meeting & Workshop |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2012 |
End | 09/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Workshop participation of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 02/2010 |
End | 02/2010 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Research Visit of Claus Koestler at University of Cardi |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2009 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Participation at Meeting of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 03/2011 |
End | 03/2011 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Workshop participation of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2010 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £300 (GBP) |
Funding ID | Presentation of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 12/2010 |
End | 12/2010 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Invited Participation at Meeting of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 04/2012 |
End | 04/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £1,000 (GBP) |
Funding ID | EU-NC- UKIERI - WIMCS Mathematical Physics Cluster Work |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 05/2011 |
End | 05/2011 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Invited Participation at Meeting of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2012 |
Description | Wales Institute of Maths & Comp Sciences |
Amount | £200 (GBP) |
Funding ID | Participation at Meeting of Claus Koestler |
Organisation | Wales Institute of Mathematical and Computational Sciences |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2009 |