Dr Gandalf Lechner

Biography

Qualifications

• 2002 Dipl. Phys. (Georg-August-Universitaet Goettingen)
• 2006 Dr. rer. nat. (Georg-August-Universitaet Goettingen)

Previous positions

• 2018-2020 - Senior Lecturer, School of Mathematics, Cardiff University
• 2015-2018 - Lecturer, School of Mathematics, Cardiff University
• 2011-2015 - Assistant in the Quantum Field Theory and Gravity group at the University of Leipzig
• 2008-2011 - 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

• Date
• Type
• Selected

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, July-Sept. 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, May-July 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 Yang-Baxter 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 "Multi-particle S-matrix models in 1+1 dimensions and associated QFTs"

Outreach material

• Braid groups, the Yang-Baxter 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:

Yang-Baxter Representations (with Ulrich Pennig and Simon Wood)
The Yang-Baxter 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 R-matrices 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.

Quantum-mechanical Backflow (with Henning Bostelmann and Daniela Cadamuro)One incarnation of the uncertainty relation is the so-called backflow effect: A quantum-mechanical 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 short-range 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)
• Yang-Baxter 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 (full-size) MFO workshop in July 2016 (with A. Abdesselam, S. Hollands, C. Kopper)
• 2011-2014 FWF-Project “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)

2020

• Yang-Baxter representations of the infinite braid group and subfactors
  UK Virtual Operator Algebras Seminar , online, October 2020

2019

• High-energy bounds on wave operators
  Mathematical Physics Seminar, Leipzig University, December 2019
• An operator-algebraic perspective on unitary R-matrices
  Mathematical Physics Seminar, University of York, November 2019
• Yang-Baxter endomorphisms
  Subfactors and Applications, Oberwolfach, October 2019
• From the construction of integrable QFTs to the classification of unitary R-matrices
  Mathematics of interacting QFT models, York, July 2019
• Deformations of quantum field theories, the construction of models, and TT-deformations
  TT- and other solvable deformations of quantum field theories , Simons Center for Geometry and Physics, Stony Brook, April 2019
• R-matrices and localised endomorphisms
  Mathematical Physics Seminar, Nottingham University, March 2019
• Quantum-mechanical 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 Yang-Baxter 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
• Quantum-mechanical backflow and scattering theory
  Conference AQFT: Where operator algebras meet microlocal analysis, Cortona, Italy, June 2018
• Yang-Baxter characters of the infinite symmetric group and subfactors
  Deformation Quantization Seminar, Würzburg, Germany, March 2018
• All involutive solutions of the Yang-Baxter 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 Yang-Baxter equation
  Advances in Mathematics and Theoretical Physics, Accademia Nazionale dei Lincei, Rome, September 2017
• Yang-Baxter Representations of the Infinite Symmetric Group
  Modern Mathematics of Quantum Theory, University of York, September 2017
• Yang-Baxter Representations of the Infinite Symmetric Group
  Foundations and Constructive Aspects of QFT, Leipzig University, June 2017
• Yang-Baxter Representations of the Infinite Symmetric Group
  Subfactors, K-theory 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 Rieffel-deformed 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 Yang-Baxter 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 operator-algebraic solution
  QFT Seminar, Oxford University , February 2016
• Constructing QFTs with modular theory and R-matrices
  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
• R-matrices and integrable QFTs
  Lie Groups: Representations and Geometry , Erlangen, September 2015
• O(d,1)-symmetric R-matrices 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 Operator-Algebraic Perspective
  Wales Mathematics Colloquium , Gregynog, May 2015
• Representations of Rieffel-deformed 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 non-commutative QFT and uniqueness of its KMS states
  Quantum Mathematical Physics , Regensburg, September 2014
  Hyperbolic PDEs with non-commutative 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
• Non-local perturbations of hyperbolic PDEs and QFT models on non-commutative spacetimes
  GEP-Seminar , Leipzig, May 2013
• Non-Local 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 low-dimensional quantum field theory , Universita Rom II Tor Vergata, October 2012
• Borchers triples and the construction of models in quantum field theory
  Memorial Symposium Hans-Juergen 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 vector-valued symbols and locally noncommutative spacetimes
  Modern Trends in Algebraic Quantum Field Theory , University of Pavia, September 2011
• Oscillatory integrals for vector-valued symbols and locally noncommutative spacetimes
  Harmonic Analysis, Deformation Quantization, Noncommutative Geometry , Scalea, Italy, September 2011
• Multiplicative deformations of the Borchers-Uhlmann 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 Borchers-Uhlmann 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 KwaZulu-Natal, 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 Rieffel-Deformationen
  Freiburg University , February 2010

Supervision

I am supervising PhD students in areas related to my own research, including

• mathematical physics, specifically quantum field theory
• von Neumann algebras
• Yang-Baxter equations and the infinite braid/symmetric groups

Current supervision

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 Morfa-Morales (joint supervision with J Yngvason, University of Vienna) - Deformations of Quantum Field Theories on Curved Spacetimes, PhD 2012