Prof. Dr. Gandalf Lechner
Lehrstuhl für Mathematik (Operatoralgebren) (Heisenberg-Professur)
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Cauerstraße 11 91058 ErlangenZimmer: 02.321, Geschoss: 02
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- from 09.2021: Full professor at the Department of Mathematics, FAU University Erlangen-Nürnberg
- 2021-2026 (extended to 2028): Heisenberg professor funded by the DPG
- 10.2018-08.2021: Head of the GAPT (Geometry, Algebra, Mathematical Physics, Topology) Research Group.
- 05.2015-08.2021: Lecturer, Senior Lecturer, Reader at the School of Mathematics, Cardiff University, in the GAPT Group
- 12.2011-04.2015: Assistant in the Quantum Field Theory and Gravity group at the University of Leipzig
- 03.2008-11.2011: Assistant in the Mathematical Physics Group at the University of Vienna
- 2006-2007 Researcher at Göttingen, Juiz de Fora, Vienna (at the Erwin Schrödinger Institute for Mathematical Physics)
- 2006 PhD in mathematical physics at Göttingen University. Supervisor: D. Buchholz.
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Conference talks (2017-today)
- Standard Subspaces
Minicourse at YMC*A 2026, Oxford, August 2026 - Unitary R-matrices, mostly with two eigenvalues
The Yang–Baxter Equation and Representations of Braid Groups, Oberwolfach, October 2025 - Discussion Session on Entropy and Modular Theory
Causal Fermion Systems 2025, Regensburg, October 2025 - Localisation Observables and Modular Theory
Operator Algebras and Mathematical Physics, ICMS Workshop, Edinburgh, September/October 2025 - Localisation Observables and Modular Theory
LQP Workshop 51 and Rainer-Fest, September 2025 - Standard Subspaces and twisted Araki-Woods subfactors
Oberwolfach meeting „Subfactors and Applictions“, Oberwolfach, July 2025 - On causal and covariant space(time) localisation observables
10th meeting of the AQFTUK network, Cardiff, June 2025 - Quantum Field Theory on a Nichols Algebra
Workshop „Quantum groups, tensor categories and quantum field theory“, Oslo, January 2025 - KMS states on Ising QFTs and crossed products
Operator Algebras in High Energy Physics, Stockholm, September 2024 - Twists and Localization Structures: Local and Non-Local Models in Quantum Field Theory
Exactly Solvable Models, ESI Vienna, July 2024 - Quantum Field Theory and Modular Theory
LQP48 and Detlev-Fest, Leipzig, June 2024 - Quantum Field Theory on a Nichols Algebra
Yang-Baxter algebras, Conference at Heriot-Watt University, Edinburgh, June 2024 - Inclusions of Standard Subspaces
Oberwolfach Mini-Workshop on Standard Subspaces in Quantum Field Theory and Representation Theory, October 2023
Proceedings contribution - Twisted Araki-Woods Factors in QFT: Modular Data and Inclusions
Developments in Modern Mathematics, Conference at Göttingen University, September 2023 - Integrable quantum field theories between modular theory and the Yang-Baxter equation
Workshop on Geometric Methods in Physics, Bialowieza, July 2023
Proceedings contribution - Standard Subspaces and Twisted Araki-Woods (Sub-)Factors
Conference Where Mathematics Meets Quantum Physics, Rome, June 2023 - Entanglement in operator-algebraic quantum field theory
Workshop on Functional Analysis and Quantum Information, ICMAT Madrid, March 2023 - Borchers Triples and their Deformations in QFT
58th Seminar Sophus Lie, Erlangen, March 2023 - Classification of unitary R-matrices by braid group characters
Workshop Skew Braces and the Yang-Baxter Equation, Oberwolfach, February 2023 - Quantum field theory without quantisation – from standard subspaces to observable algebras
16th Colloquium “Mathematics and Foundations of Quantum Theory”, Regensburg, February 2023 - Local and non-local half-sided modular inclusions
Conference „Energy conditions in quantum field theory“, Leipzig, September 2022 - Local and non-local CFTs on the line and subfactors of type III
Conference „Operator Algebras: Subfactors, K-theory, Conformal Field Theory“, Gregynog, August 2022 - Unitary solutions of the Yang-Baxter equation and von Neumann algebras
Conference „The algebra of the Yang-Baxter equation“, Będlewo conference center, July 2022 - Singular half-sided modular inclusions and deformation quantization
IWOTA Lancaster (virtual) , online, August 2021
Slides - 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 T\overline{T}-deformations
T\overline{T} and other solvable deformations of quantum field theories , Simons Center for Geometry and Physics, Stony Brook, April 2019 - Braid group characters and localised endomorphisms
43rd LQP workshop „Foundations and Constructive Aspects of QFT“ , Galieo Galilei Institute Firenze, February 2019 - Quantum-mechanical backflow and scattering
Algebraic Quantum Field Theory: Where Operator Algebra meets Microlocal Analysis , Cortona, Italy, June 2018 - Modular Localization and Constructive Algebraic QFT
Reflection Positivity , November 2017, Workshop at the Oberwolfach Research Center - All involutive solutions of the Yang-Baxter equation
Advances in Mathematics and Theoretical Physics , September 2017, Accademia Nazionale dei Lincei, Roma
Slides - Yang-Baxter Representations of the Infinite Symmetric Group
Modern Mathematics of Quantum Theory , September 2017, York University - Yang-Baxter Representations of the Infinite Symmetric Group
LQP Workshop 40 , June 2017, Leipzig University / MPI - Yang-Baxter Representations of the Infinite Symmetric Group
Subfactors Programme, Workshop III , June 2017, Newton Institute, Cambridge
Past conference talks (2004-2016)
- Sigma models in algebraic QFT
Local Quantum Physics and Beyond: In Memoriam Rudolf Haag , Hamburg, September 2016 - SO(d,1)-invariant Yang-Baxter operators and a dS/CFT correspondence
Operator Algebras and Quantum Field Theory , Frascati, June 2016 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - Star products on Hilbert space
Bayrischzell workshop , Bayrischzell, May 2010 - Rieffel deformations and the construction of local nets
Conference of Noncommutative geometry EU network , Copenhagen, October 2009 - Deformations of Operator Algebras and the Construction of Quantum Field Theories
ICMP 2009, Operator Algebras Session , Prague, August 2009 - Deformations of Operator Algebras and the Construction of Quantum Field TheoriesMovie recording of talk
Algebraic Quantum Field Theory – The first 50 years , Goettingen, July 2009 - Star products and deformation procedures in quantization, non-commutative geometry and quantum field theory
Local Quantum Physics workshop 24 , Leipzig, June 2009 - Field Deformations vs Lagrangian Deformations in Noncommutative QFT
Workshop on Noncommutative Geometry and Quantum Field Theory , Chennai, December 2008 - Noncommutative Deformations of Quantum Field Theories
Mini-workshop on Noncommutative Geometry and Quantum Field Theory , Rome, October 2008 - Noncommutative Deformations of Wightman Quantum Field Theories
Operator Algebras and Conformal Field Theory, ESI program , Vienna, September 2008 - Noncommutative Deformations of Quantum Fields
Meeting of the Noncommutative Geometry EU Network , DIAS Dublin, June 2008 - Models of Wedge-Local Quantum Fields
DPG Conference , Freiburg, March 2008 - Wedge-local Quantum Fields, Non-Commutative Minkowski Space, and Interaction
4th Vienna Central European Seminar: Commutative and Noncommutative Quantum Fields , Vienna University, December 2007 - Wedge-Local Quantum Fields and Noncommutative Minkowski Space
Workshop on Noncommutative Geometry, , Bratislava, July 2007 - Wedge-Localized Quantum Fields and Noncommutative Minkowski Space
Local Quantum Physics Workshop 20 , Leipzig, June 2007 - Towards the Construction of the O(N)-Sigma models
ESI Programme „Mathematical and Physical Aspects of Perturbative Approaches to Quantum Field Theory“ , Vienna, March 2007 - Construction of asymptotically complete interacting quantum field theories in two dimensions
ICMP 2006, Young Researchers Symposium , Rio de Janeiro, August 2006 - Construction of Asymptotically Complete Interacting Quantum Field Theories in Two Dimensions
Topics in Mathematical Physics , Sao Paulo, August 2006 - Constructing local nets of von Neumann algebras from their S-matrices
Brazilian Operator Algebras Conference , Florianopolis, July 2006 - The inverse scattering problem for factorizing S-matrices
DESY Theory Colloquium , Hamburg, May 2006 - Constructing Local Nets from an S-matrix
South Eastern Analysis Meeting (SEAM XXII) , Gainesville, USA, March 2006 - Constructing Integrable Models in Algebraic Quantum Field Theory
Local Quantum Physics Workshop 17 , Goettingen, December 2005 - Geometric Modular Action in Quantum Field Theory and Quantum Field Theories from Geometric Modular Action
Oberwolfach Meeting „Noncommutative Geometry and Quantum Field Theory“ , Oberwolfach, October 2005 - Nuclearity Properties of Theories with a Factorizing S-Matrix
Conference Rigorous Quantum Field Theory in honour of Jacques Bros , Saclay, July 2004 - Polarization-Free Quantum Fields and Interaction
DPG Conference, Session „Noncommutative Geometry and Quantum Field Theory“ , Ulm, March 2004
Seminar talks (2017-today)
- Localisation Observables
Mathematical Physics Seminar, University of Trento, May 2026 - Integrable quantum field theories — inverse scattering, braided vector spaces, and local algebras
Mathematical Physics Seminar, University of Vienna, December 2025 - Inclusions of Standard Subspaces
Operator Algebras Seminar, University of Rome Tor Vergata, Rome, October 2025 - Localisation Observables
Würzburg Mathematical Physics Seminar, May 2025 - Modular Structure and Inclusions of Twisted Araki-Woods Algebras
Berkeley Probabilistic Operator Algebra Seminar, online, January 2023
Slides - Deformations of Araki-Woods Algebras
Deformation Quantization Seminar, Würzburg, January 2023 - A review of algebraic constructive quantum field theory
Quantum Gravity Seminar, FAU, June 2022 - Unitary braidings
Emmy Noether Seminar, FAU, May 2022 - Integrable quantum field theories – Inverse scattering, local von Neumann algebras, asymptotic completeness
IFS seminar Gent, April 2022 - Half-sided modular inclusions and the algebra at infinity
GEP Seminar, Leipzig University, January 2022 - Constructions of conformal QFTs from Borchers triples: non-local examples
Mathematical Physics Seminar, Regensburg University, December 2021 - Singular half-sided modular inclusions and the algebra at infinity
Deformation Quantization Seminar, Würzburg University, online, July 2021 - Yang-Baxter representations of the infinite braid group and subfactors
UK Virtual Operator Algebras Seminar , online, October 2020 - An operator-algebraic perspective on unitary R-matrices
Mathematical Physics Seminar , University of York, November 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 - The Yang-Baxter equation and extremal characters of the infinite braid group
Mathematical Physics Seminar, Leipzig University , December 2018 - Algebraic Quantum Field Theory
GAPT Seminar, Cardiff University , March 2018 - Yang-Baxter characters of the infinite symmetric group and subfactors
Deformation Quantization Seminar, Universität Würzburg , March 2018 - All involutive solutions of the Yang-Baxter equation
Séminaire de physique mathématique, Institut Camille Jordan, Lyon , March 2018 - Quantum backflow and scattering theory
Mathematical Physics Seminar, Imperial College London , May 2017 - Quantum Backflow and Scattering
Mathematical Physics Seminar, University of York , February 2017 - Integrable QFTs 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
Past seminar talks (2004-2016)
- Quantum-Mechanical Backflow and ScatteringPhysics Seminar, Cardiff University , November 2016
- Modular NuclearityMath. Phys. Seminar, York University , March 2016
- The inverse scattering problem for integrable QFTs in 2d and its operator-algebraic solutionQFT Seminar, Oxford University , February 2016
- Constructing QFTs with modular theory and R-matricesGraduiertenkolleg Mathematik+Physik, Universität Göttingen , February 2016
- Singular values of Hardy space operators and relative commutants of von Neumann algebrasGeometry and Analysis Seminar, Queen Mary, London , December 2015
- Wave Equations with Noncommutative TimeMathematical Physics Seminar, University of York , June 2015
- Noncommutative Wave EquationsMathematical Physics Seminar, Bristol University , May 2015
- KMS functionals and KMS states for algebras of deformed quantum fieldsDeformation Quantization Seminar, Uni Würzburg , November 2013
- Equivalence of two deformation schemes in QFTEssays in low-dimensional quantum field theory , Universita Rom II Tor Vergata, October 2012
- Deformations of Quantum Field TheoriesLeipzig University , June 2010
- Deformation techniques in quantization and quantum field theoryHamburg University , June 2010
- Deformations of quantum field theoriesYork University , June 2010
- Warped Convolutions und Rieffel-DeformationenFreiburg University , February 2010
- Rieffel-Deformationen und die Konstruktion von wechselwirkenden QuantenfeldtheorienFreiburg University , July 2009
- Nicht-kommutative Deformationen von QuantenfeldtheorienLMU Munich , May 2008
- Quantum Fields on the Non-Commutative Minkowski Space : Scattering, Thermal Equilibrium and CausalityLaboratoire de Physique Theorique , Orsay, March 2008
- The inverse scattering problem for quantum field theories with factorizing S-matricesSlidesEcole Polytechnique , Palaiseau, March 2008
- Modular Theory and Quantum Field TheoryAustralian National University , Canberra, February 2008
- Wedge-Local Quantum Fields in Integrable and Nonlocal ModelsUniversita Tor Vergata , Rome, January 2008
- The inverse scattering problem for Quantum Field Theories with Factorizing S-MatricesMath. Phys. Seminar, ETH Zurich , October 2007
- Construction of local nets from a wedge algebraOperator Algebras Seminar, University of Tokyo , October 2007
- Local nets of von Neumann algebras and modular theoryOperator Algebras Seminar, University of Tokyo , October 2007
- Construction of Quantum Field Theories with Factorizing S-Matrices, IESI Seminar , Vienna, November 2006
- The inverse scattering problem for factorizing S-matricesSeminario do DF-UFJF , Juiz de Fora, Brazil, August 2006
- The inverse scattering problem for factorizing S-matricesDESY Theory Colloquium , Hamburg, May 2006