Dr Gandalf Lechner
Reader
 lechnerg@cardiff.ac.uk
 +44(0)29 208 70943
 M/2.18, Maths and Education Building , Senghennydd Road, Cardiff, CF24 4AG
 Available for postgraduate supervision
Overview
Research interests
My research focusses on operator algebras and their applications to conceptual and mathematical problems arising in quantum field theory. I am particularly interested in new approaches to the problem of rigorously constructing quantum field theory models. A novel line of research addresses this question via operatoralgebraic deformations of quantum field theories, a topic also connected to noncommutative geometry and quantum field theory on noncommutative spaces.
Further interests include integrable models in quantum field theory and related structures, such as the YangBaxter equation, braid group representations and questions in Operator Theory that arise in the study of spaces of holomorphic functions.
For more details about my research, you can have a look at my publications and research pages.
Administrative Roles
 Head of the GAPT Research Group, School of Mathematics
 Member of School Research Committee
External Positions
 Member of the Committee of the Mathematical Physics Group of the IoP
 Member of the Committee of the Mathematical Physics Group of the DPG
 INIICMS correspondent for the IoP
Professional Memberships
 IAMP  International Association for Mathematical Physics
 LMS  London Mathematical Society
 IoP  Institute of Physics
 DPG  Deutsche Physikalische Gesellschaft
 Fellow of the Higher Education Academy HEA
Research group
GAPT (Geometry, Algebra, Mathematical Physics and Topology) Research Group
Personal website
Biography
Qualifications
 2002 Dipl. Phys. (GeorgAugustUniversitaet Goettingen)
 2006 Dr. rer. nat. (GeorgAugustUniversitaet Goettingen)
Previous positions
 20182020  Senior Lecturer, School of Mathematics, Cardiff University
 20152018  Lecturer, School of Mathematics, Cardiff University
 20112015  Assistant in the Quantum Field Theory and Gravity group at the University of Leipzig
 20082011  Assistant in the Mathematical Physics Group at the University of Vienna
 2007  "Experienced Researcher" in the Marie Curie Research Training network “Quantum Spaces – Noncommutative Geometry” at its Vienna node
 2007  Junior Research Fellow at the Erwin Schroedinger Institute for Mathematical Physics, Vienna
 2006  PostDoc in the DFG research project "Modular Structure and Particle Aspects of Quantum Field Theory" at Goettingen University
Publications
2021
 Bostelmann, H., Cadamuro, D. and Lechner, G. 2021. High energy bounds on wave operators. Journal of Operator Theory 86(1), pp. 6191. (10.7900/jot.2020feb01.2285)
 Lechner, G. 2021. Zopfgruppen, die YangBaxtergleichung, und unterfaktoren. Snapshots of modern mathematics from Oberwolfach 2021, article number: 5. (10.14760/SNAP2021005DE)
2020
 Lechner, G. and Scotford, C. 2020. Fock representations of ZF algebras and Rmatrices. Letters in Mathematical Physics 110, pp. 16231643. (10.1007/s11005020012713)
 Conti, R. and Lechner, G. 2020. YangBaxter endomorphisms. Journal of the London Mathematical Society 103(2), pp. 633671. (10.1112/jlms.12387)
2019
 Lechner, G., Pennig, U. and Wood, S. 2019. YangBaxter representations of the infinite symmetric group. Advances in Mathematics 355, article number: 106769. (10.1016/j.aim.2019.106769)
 Lechner, G. 2019. Subfactors and unitary Rmatrices. Presented at: Subfactors and Applications, Oberwolfach, Germany, 27 october  2 November 2019. pp. .
2018
 Lechner, G.et al. 2018. Approximation numbers of weighted composition operators. Journal of Functional Analysis 274(7), pp. 19281958. (10.1016/j.jfa.2018.01.010)
 Hollands, S. and Lechner, G. 2018. SO(d,1)invariant YangBaxter operators and the dS/CFT correspondence. Communications in Mathematical Physics 357, pp. 159202. (10.1007/s0022001729426)
2017
 Alazzawi, S. and Lechner, G. 2017. Inverse scattering and locality in integrable quantum field theories. Communications in Mathematical Physics 354(3), pp. 913956. (10.1007/s0022001728910)
 Bostelmann, H., Cadamuro, D. and Lechner, G. 2017. Quantum backflow and scattering. Physical Review a 96(1), article number: 12112. (10.1103/PhysRevA.96.012112)
2016
 Abdesselam, A.et al. 2016. Recent mathematical developments in quantum field theory. Oberwolfach Reports 13(3), pp. 20692122. (10.4171/OWR/2016/36)
 Lechner, G. and Waldmann, S. 2016. Strict deformation quantization of locally convex algebras and modules. Journal of Geometry and Physics 99, pp. 111144. (10.1016/j.geomphys.2015.09.013)
 Lechner, G. and Sanders, K. 2016. Modular nuclearity: a generally covariant perspective. Axioms 5(1), article number: 5. (10.3390/axioms5010005)
2015
 Lechner, G. and Verch, R. 2015. Linear hyperbolic PDEs with noncommutative time. Journal of Noncommutative Geometry 9(3), pp. 9991040. (10.4171/JNCG/214)
 Lechner, G. 2015. Algebraic constructive quantum field theory: Integrable models and deformation techniques. In: Brunetti, R. et al. eds. Advances in Algebraic Quantum Field Theory. Springer, pp. 397448.
 Lechner, G. and Longo, R. 2015. Localization in nets of standard spaces. Communications in Mathematical Physics 336, pp. 2761. (10.1007/s0022001421992)
2014
 Lechner, G. and Schützenhofer, C. 2014. Towards an operatoralgebraic construction of integrable global gauge theories. Annales Henri Poincare 15(4), pp. 645678. (10.1007/s000230130260x)
 Lechner, G. and Schlemmer, J. 2014. Thermal equilibrium states for quantum fields on noncommutative spacetimes. Presented at: Quantum Mathematical Physics, Regensburg, Germany, 29 September  2 October 2014 Presented at Finster, F. et al. eds.Quantum Mathematical Physics: A Bridge between Mathematics and Physics. Springer, (10.1007/9783319269023)
2013
 Lechner, G., Schlemmer, J. and Tanimoto, Y. 2013. On the equivalence of two deformation schemes in quantum field theory. Letters in Mathematical Physics 103(4), pp. 421437. (10.1007/s1100501205999)
 Grosse, H.et al. 2013. Wick rotation for quantum field theories on degenerate Moyal space(time). Journal of Mathematical Physics 54(2), article number: 22307. (10.1063/1.4790886)
2012
 Lechner, G. 2012. Deformations of quantum field theories and integrable models. Communications in Mathematical Physics 312(1), pp. 265302. (10.1007/s002200111390y)
2011
 Dappiaggi, C., Lechner, G. and MorfaMorales, E. 2011. Deformations of quantum field theories on spacetimes with killing vector fields. Communications in Mathematical Physics 305(1), pp. 99130. (10.1007/s0022001112104)
 Bostelmann, H., Lechner, G. and Morsella, G. 2011. Scaling limits of integrable quantum field theories. Reviews in Mathematical Physics 23(10), article number: 1115. (10.1142/S0129055X11004539)
2010
 Buchholz, D., Lechner, G. and Summers, S. J. 2010. Warped convolutions, rieffel deformations and the construction of quantum field theories. Communications in Mathematical Physics 304(1), pp. 95123. (10.1007/s0022001011371)
2009
 Lechner, G. 2009. Deformations of operator algebras and the construction of quantum field theories. Presented at: XVI International Congress on Mathematical Physics 2009, Prague, 3  8 September 2009.
2008
 Lechner, G. 2008. Construction of quantum field theories with factorizing Smatrices. Communications in Mathematical Physics 277(3), pp. 821860. (10.1007/s0022000703815)
 Grosse, H. and Lechner, G. 2008. Noncommutative deformations of Wightman quantum field theories. Journal of High Energy Physics 2008(9), article number: 131. (10.1088/11266708/2008/09/131)
2007
 Lechner, G. 2007. Towards the construction of quantum field theories from a factorizing Smatrix. Progress in Mathematics Boston 251, pp. 175197. (10.1007/9783764374341_13)
 Grosse, H. and Lechner, G. 2007. Wedgelocal quantum fields and noncommutative minkowski space. Journal of High Energy Physics 2007(11), article number: 12. (10.1088/11266708/2007/11/012)
2005
 Lechner, G. 2005. On the existence of local observables in theories with a factorizing Smatrix. Journal of Physics A: Mathematical and General 38(13), pp. 3045. (10.1088/03054470/38/13/015)
2004
 Buchholz, D. and Lechner, G. 2004. Modular Nuclearity and Localization. Annales Henri Poincaré 5(6), pp. 10651080. (10.1007/s0002300401908)
2003
 Lechner, G. 2003. Polarizationfree quantum fields and interaction. Letters in Mathematical Physics 64, pp. 137154.
Teaching
Undergraduate modules
In the academic year 2020/21 I am teaching the following modules. Details on on/offline teaching will be communicated in due course.
 MA2008 Linear Algebra II
 MA0414 Mathematical Foundations of Quantum Physics
Overview video for prospective students:
https://youtu.be/2KgcFLFqPmE
Previously taught modules:
 MA01005 Foundations of Mathematics I (2017/18, 2018/19, 2019/20)
 MA0322 Knots (2015/16)
 MA0414 Mathematical Foundations of Quantum Physics (2016/17, 2017/18, 2018/19, 2019/20)
Supervision of undergraduate projects
(see tab "Supervision" for PhD projects)
 Alexander Curis (MMATH project, Cardiff 2020/21)
Project: "Quantum Entanglement and Operator Algebras"  Timothy Weaving (MMATH project, Cardiff 2019/20)
Project: "On Quantifying the Quantum Entanglement Present Within Shor's Algorithm"  Owen Tanner (CUROP research student, Cardiff, JulySept. 2019, supervised jointly with Ulrich Pennig)
Project "Von Neumann Algebras and Applications"  Charley Scotford (MMATH project, Cardiff, 2016/17)
Project "Supersymmetric quantum mechanics"  Nathaniel Fox (MMATH project, Cardiff, 2016/17)
Project "Transparent potentials for 1d quantum scattering"  Vidal Agniel (Internship student from Rennes, France, MayJuly 2016)
worked on composition operators on Hilbert spaces of analytic functions  Giovanni Cattarina (Erasmus student from Bologna, Italy, 2015/16)
Laurea thesis: "Link Invariants, Braid Groups and Classification of Enhanced YangBaxter Operators in d=2"  Peter Sutherns (MMATH project, Cardiff, 2015/16)
Project: "The Radon Transform"  Albert Huber (Diploma 2012, Vienna)
Project "Thermal Equilibrium States in Deformed Quantum Field Theory"  Christian Schützenhofer (Diploma 2011, Vienna)
Project "Multiparticle Smatrix models in 1+1 dimensions and associated QFTs"
Outreach material
 Braid groups, the YangBaxter equation, and subfactors, February 2020
 This is a contribution to the series Snapshots of Modern Mathematics published by the Oberwolfach Research Institute for Mathematics which aims to explain mathematical problems and ideas of present relevance in an accessible and understandable way to a wide audience. For a German version, see here.
 Visual Mathematics: Braids and Knots
A short video for prospective mathematics students, produced for our virtual open day in July 2020
braids and knots video
Some recent research of mine is:
YangBaxter Representations (with Ulrich Pennig and Simon Wood)
The YangBaxter equation appears in a remarkable number of different fields, such as statistical mechanics, knot theory, quantum groups. quantum field theory, quantum mechanics, quantum information theory, subfactors, … . This equation is very hard to solve directly, and the structure of the set of its solutions is insufficiently understood. We considered the case of involutive solutions R, i.e. those Rmatrices that square to the identity. In this case, we found a complete classification of all solutions up to a natural equivalence suggested by applications in quantum field theory.
Quantummechanical Backflow (with Henning Bostelmann and Daniela Cadamuro)One incarnation of the uncertainty relation is the socalled backflow effect: A quantummechanical particle in one spatial dimension that has positive momentum (with probability 1) may still have negative probability flux, i.e. the probability can flow in the direction opposite to the momentum. We investigated the backflow effect for interacting systems governed by an arbitrary shortrange potential. It turns out that backflow is a universal effect that exists in any such system, and its magnitude can be estimated by analytic methods.
Constructive Algebraic Quantum Field TheoryIn 2015, I wrote a book chapter reviewing the status of constructive algebraic quantum field theory.
Conferences organised
 Online Lecture Series “An Introduction to Quantum Field Theory in Curved Spacetime” by Daniel Siemssen and Matteo Capoferri (an event of our AQFTUK network), October 2020
 LQP Colloquium, since Sept. 2020 (with S. Hollands, Y. Kawahigashi, R. Longo, K.H. Rehren)
 Virtual LQP1 / LQP45 online workshop, June 2020 (with P. Naaijkens)
 Operator Algebras and Quantum Physics. Programme and workshop at the Simons Center for Geometry and Physics, June 2019 (with S. Hollands, V. Jones, R. Longo)
 ICFT 22  22nd UK Meeting on Integrable Models, Conformal Field Theory and Related Topics, Cardiff, June 2018 (with S. Wood)
 Algebraic Structures & Quantum Physics, LMS Regional Meeting for South West and South Wales, Cardiff, December 2017 (with M. Pugh and S. Wood)
 Quantum Field Theory: Concepts, Constructions, and Curved Spacetimes, York, April 2017 (with D. Bahns and C. Fewster)
 YangBaxter Equations: A Tangle of Physics & Mathematics, Workshop in Cardiff, December 2016 (with U. Pennig and S. Wood)
 Recent Mathematical Developments in Quantum Field Theory, Oberwolfach, 2016 (with A. Abdesselam S. Hollands, C. Kopper)
 Session "Operator Algebras and Quantum Field Theory" at the 14th Marcel Grossmann meeting, Universita La Sapienza, July 2015 (with G. Ruzzi)
 LQP 31 – Workshop “Foundations and Constructive Aspects of QFT”, Leipzig University, November 2012 (with R. Verch)
 Rigorous quantum field theory in the LHC era, ESI Vienna, September 2011 (with C. Jaekel and C. Kopper)
Grant income (since 2010)
 2020 EPSRC grant, £ 18,585 (with U. Pennig and M. Pugh)
 2018 LMS Research in Pairs Grant for a research visit to Rome, £ 941
 2018 IoP Grant for funding a workshop (ICFT22) at Cardiff, June 2018, £ 750 (with S. Wood)
 2018 LMS Grant for supporting a workshop (ICFT22) at Cardiff, June 2018, £ 2,200 (with S. Wood)
 2017 Grant from the Simons Foundation for a programme and workshop at the Simons Center in May/June 2019, ~$80,000 (with S. Hollands, V. Jones, R. Longo)
 2017 LMS grant for a conference in Cardiff, December 2017, £ 5,000 (with M. Pugh and S. Wood)
 2017 IoP grant for supporting a conference in Cardiff, December 2017, £ 750 (with M. Pugh and S. Wood)
 2017 IoP grant for supporting a conference in York, April 2017, £ 1,000 (with D. Bahns and C. Fewster)
 2017 LMS research in pairs grant for a research visit to York, £ 410
 2016 IoP grant for a workshop at Cardiff, £ 1,200 (with U. Pennig and S. Wood)
 2016 Oberwolfach Grant for running a (fullsize) MFO workshop in July 2016 (with A. Abdesselam, S. Hollands, C. Kopper)
 20112014 FWFProject “Deformations of Quantum Field Theories”, together with J. Yngvason (PI), € 360,000
 2011 ESI Grant for organizing a conference at the Erwin Schrödinger Institute in Vienna, € 24,000, with C. Kopper and C. Jäkel
Talks (since 2010)
2021

Singular halfsided modular inclusions and the algebra at infinity
Deformation Quantization Seminar, online, July 2021
2020
 YangBaxter representations of the infinite braid group and subfactors
UK Virtual Operator Algebras Seminar , online, October 2020
2019
 Highenergy bounds on wave operators
Mathematical Physics Seminar, Leipzig University, December 2019  An operatoralgebraic perspective on unitary Rmatrices
Mathematical Physics Seminar, University of York, November 2019  YangBaxter endomorphisms
Subfactors and Applications, Oberwolfach, October 2019  From the construction of integrable QFTs to the classification of unitary Rmatrices
Mathematics of interacting QFT models, York, July 2019  Deformations of quantum field theories, the construction of models, and TTdeformations
TT and other solvable deformations of quantum field theories , Simons Center for Geometry and Physics, Stony Brook, April 2019  Rmatrices and localised endomorphisms
Mathematical Physics Seminar, Nottingham University, March 2019  Quantummechanical backflow and scattering
Mathematical Physics Seminar , Northumbria University, Newcastle, March 2019  Braid group characters and localised endomorphisms
43rd LQP workshop "Foundations and Constructive Aspects of QFT" , Galieo Galilei Institute Firenze, February 2019
2018
 The YangBaxter equation and extremal characters of the infinite braid group
Mathematical Physics Seminar, Leipzig University, December 2018  TBA
Conference Physics and Mathematics of Quantum Field Theory, Banff Research Station, Canada, July/August 2018  Quantummechanical backflow and scattering theory
Conference AQFT: Where operator algebras meet microlocal analysis, Cortona, Italy, June 2018  YangBaxter characters of the infinite symmetric group and subfactors
Deformation Quantization Seminar, Würzburg, Germany, March 2018  All involutive solutions of the YangBaxter equation
Seminaire de Physique Mathématique, Lyon, France, March 2018
2017
 Modular Localization and Constructive Algebraic QFT
Workshop on Reflection Positivity, Oberwolfach Research Centre, November 2017  All involutive solutions of the YangBaxter equation
Advances in Mathematics and Theoretical Physics, Accademia Nazionale dei Lincei, Rome, September 2017  YangBaxter Representations of the Infinite Symmetric Group
Modern Mathematics of Quantum Theory, University of York, September 2017  YangBaxter Representations of the Infinite Symmetric Group
Foundations and Constructive Aspects of QFT, Leipzig University, June 2017  YangBaxter Representations of the Infinite Symmetric Group
Subfactors, Ktheory and conformal field theory, Newton Institute Cambridge, June 2017  Quantum Backflow and Scattering Theory
Mathematical Physics Seminar, Imperial College, May 2017  Quantum Backflow and Scattering
Mathematical Physics seminar, University of York, February 2017  Integrable quantum field theories and von Neumann algebras
Theoretical Physics Seminar, King's College, London, February 2017  Representations of Rieffeldeformed C*algebras and deformations of Borchers triples
Analysis Seminar, Glasgow University, January 2017
2016
 Quantum Backflow and Scattering Theory
Physics Seminar, Cardiff University , November 2016  Sigma models in algebraic QFT
Local Quantum Physics and Beyond: In Memoriam Rudolf Haag , Hamburg, September 2016  SO(d,1)SO(d,1)invariant YangBaxter operators and a dS/CFT correspondence
Operator Algebras and Quantum Field Theory , Frascati, June 2016  Modular Nuclearity
Math. Phys. Seminar, York University , March 2016  The inverse scattering problem for integrable QFTs in 2d and its operatoralgebraic solution
QFT Seminar, Oxford University , February 2016  Constructing QFTs with modular theory and Rmatrices
Graduiertenkolleg Mathematik+Physik, Universität Göttingen , February 2016
2015
 Singular values of Hardy space operators and relative commutants of von Neumann algebras
Geometry and Analysis Seminar, Queen Mary, London , December 2015  Rmatrices and integrable QFTs
Lie Groups: Representations and Geometry , Erlangen, September 2015  O(d,1)symmetric Rmatrices and QFT models
Operator Algebras and Quantum Physics , Sao Paulo, July 2015  Wave Equations with Noncommutative Time
Mathematical Physics Seminar, University of York , June 2015  Noncommutative Wave Equations
Mathematical Physics Seminar, Bristol University , May 2015  Integrable Quantum Field Theories from an OperatorAlgebraic Perspective
Wales Mathematics Colloquium , Gregynog, May 2015  Representations of Rieffeldeformed C*algebras and deformations of inclusions
Workshop on Deformation Quantization: Between Formal and Strict , Oberwolfach, February 2015  Modular Structure of Generalized Free Fields and Nets of Standard Subspaces
AQFT 2015  Workshop on New Trends in Algebraic Quantum Field Theory , Frascati, February 2015
2014
 Reflection Positivity and Operator Algebras in Quantum Field Theory
Oberwolfach Workshop: Reflection Positivity in Representation Theory, Stochastics, and Physics , Oberwolfach, December 2014  The structure of the field algebra in noncommutative QFT and uniqueness of its KMS states
Quantum Mathematical Physics , Regensburg, September 2014
Hyperbolic PDEs with noncommutative time
Frontiers in Fundamental Physics , Marseille, July 2014  Operator algebras and the construction of models in quantum field theory
FJIM 2014 , Bilbao, July 2014  Construction of quantum field theories by deformation techniques
DPG Spring Conference , Berlin, March 2014
2013
 KMS functionals and KMS states for algebras of deformed quantum fields
Deformation Quantization Seminar, Uni Würzburg , November 2013  Nonlocal perturbations of hyperbolic PDEs and QFT models on noncommutative spacetimes
GEPSeminar , Leipzig, May 2013  NonLocal Perturbations of Hyperbolic PDEs and QFT on Noncommutative Spacetimes
Mathematics and Quantum Physics , Accademia dei Lincei, Rome, July 2013  Hyperbolic PDEs with star product potentials
GEOQUANT 2013 , ESI Vienna, August 2013
2012
 Equivalence of two deformation schemes in QFT
Essays in lowdimensional quantum field theory , Universita Rom II Tor Vergata, October 2012  Borchers triples and the construction of models in quantum field theory
Memorial Symposium HansJuergen Borchers "A Life for Relativistic Quantum Field Theory" , Goettingen, October 2012  KMS states of deformed quantum field theories
Algebraic Quantum Field Theory and Local Symmetries , Hausdorff Research Institute for Mathematics, Sept. 2012  Thermal Equilibrium States for QFTs on Moyal Minkowski Spacetime
ICMP 2012 , Aalborg, August 2012  Constructive algebraic quantum field theory at the example of integrable models
Mathematical Aspects of Quantum Field Theory and Quantum Statistical Mechanics , DESY, Hamburg, July 2012  Quantum field theory on locally noncommutative spacetimes
DPG Spring Conference 2012 , Goettingen, February 2012  Locally Noncommutative Spacetimes and Quantum Field Theory
Planckland , SISSA, Trieste, February 2012
2011
 QFT on locally noncommutative spacetimes
Vienna Math. Phys. Seminar , Vienna University, October 2011  Algebraic quantum field theory: From structural analysis to the construction of models
Quantum Gravity Colloquium 6 , University of Erlangen, October 2011  Oscillatory integrals for vectorvalued symbols and locally noncommutative spacetimes
Modern Trends in Algebraic Quantum Field Theory , University of Pavia, September 2011  Oscillatory integrals for vectorvalued symbols and locally noncommutative spacetimes
Harmonic Analysis, Deformation Quantization, Noncommutative Geometry , Scalea, Italy, September 2011  Multiplicative deformations of the BorchersUhlmann algebra
Local Quantum Physics workshop 28 , Goettingen, July 2011  Local and covariant deformations of quantum field theories
Quantum Theory and Gravitation , Zurich, June 2011  Multiplicative deformations of the BorchersUhlmann algebra
WIMCS workshop on quantum field theory , University Cardiff, April 2011
2010
 Deformations of Quantum Field Theories
Vienna Lunch Seminar , Vienna University, December 2010  Local and covariant deformations of observable algebras in QFT
Deformation Methods in Mathematics and Physics , Oberwolfach, September 2010  Deformations of Quantum Field Theories
NITheP Workshop  Quantum Field Theory on Curved Spacetime , University of KwaZuluNatal, Durban, August 2010  Deformations of Quantum Field Theories
Leipzig University , June 2010  Deformation techniques in quantization and quantum field theory
Hamburg University , June 2010  Deformations of quantum field theories
York University , June 2010  Star products on Hilbert space
Bayrischzell workshop , Bayrischzell, May 2010  Deformation Quantization and Deformations of Quantum Field Theories
Math. Phys. Seminar , Vienna University, March 2010  Warped Convolutions und RieffelDeformationen
Freiburg University , February 2010
Supervision
I am supervising PhD students in areas related to my own research, including
 von Neumann algebras and subfactors and their applications to quantum physics
 YangBaxter equations and the infinite braid/symmetric groups
Current supervision
Charley Scotford
Research student
Tasarla Deadman
Research student
Past projects
 Sabina Alazzawi (joint supervision with J Yngvason, University of Vienna)  Deformations of Quantum Field Theories and the Construction of Interacting Models, PhD 2014
 Thomas Ludwig (joint supervision with R Verch, University of Leipzig)  Wick Rotation for Quantum Field Theories on Degenerate Moyal Space, PhD 2013
 Eric MorfaMorales (joint supervision with J Yngvason, University of Vienna)  Deformations of Quantum Field Theories on Curved Spacetimes, PhD 2012