# Prof. Dr. Raimar Wulkenhaar, Mathematisches Institut

Member of CRC 1442 Geometry: Deformations and RigidityInvestigator in Mathematics Münster

Investigator in Mathematics Münster

Private Homepage | http://www.uni-muenster.de/MathPhys/u/raimar/ |

Research Interests | Mathematical Physics Quantum field theory Noncommutative geometry |

Selected Publications | • Grosse H, Wulkenhaar R Power-counting theorem for non-local matrix models and renormalisation. Communications in Mathematical Physics Vol. 254 (1), 2005, pp 91-127 online• Krajewski T, Wulkenhaar R Perturbative quantum gauge fields on the noncommutative torus. International Journal of Modern Physics A Vol. 15 (7), 2000, pp 1011-1029 online• Rivasseau V, Vignes-Tourneret F, Wulkenhaar R Renormalisation of noncommutative \phi^4-theory by multi-scale analysis
. Communications in Mathematical Physics Vol. 262 (3), 2006, pp 565-594 online• Grosse H, Wulkenhaar R Renormalisation of \phi^4-theory on noncommutative R^4 in the matrix base
. Communications in Mathematical Physics Vol. 256 (2), 2005, pp 305-374 online• Grosse H, Wulkenhaar R Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory. to appear in Commun. Math. Phys.Communications in Mathematical Physics Vol. 329 (3), 2014 online• Wulkenhaar R Quantum field theory on noncommutative spaces. Advances in Noncommutative Geometry, 2019, pp 607-690 online• Schürmann J, Wulkenhaar R An algebraic approach to a quartic analogue of the Kontsevich model. Vol. 2022, 2022 online• Panzer E, Wulkenhaar R Lambert-W solves the noncommutative \Phi^4-model. Communications in Mathematical Physics Vol. 374, 2020, pp 1935-1961 online• Grosse H, Hock A, Wulkenhaar R Solution of all quartic matrix models. , 2019 online• Branahl J, Hock A, Wulkenhaar R Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures. Communications in Mathematical Physics Vol. 393, 2022 online |

Selected Projects | • CRC 478 E04 - Noncommutative geometry and quantisation of physical interactions The aim is to intensify previous research on the intersection of noncommutative geometry with quantum models for physical interactions. This includes the endeavour to renormalise gauge theories on noncommutative geometries on one hand and the analysis of a noncommutative algebra of loops related to quantum gravity on the other hand. Spectral triples play an important rˆole in both directions and a central question is to construct a Dirac operator with the physically desired properties. online• RTG 2149 - Srong and Weak Interactions - from Hadrons to Dark Matter The Research Training Group (Graduiertenkolleg) 2149 "Strong and Weak Interactions - from Hadrons to Dark Matter" funded by the Deutsche Forschungsgemeinschaft focuses on the close collaboration of theoretical and experimental nuclear, particle and astroparticle physicists further supported by a mathematician and a computer scientist. This explicit cooperation is of essence for the PhD topics of our Research Training Group. Scientifically this Research Training Group addresses questions at the forefront of our present knowledge of particle physics. In strong interactions we investigate questions of high complexity, such as the parton distributions in nuclear matter, the transition of the hot quark-gluon plasma into hadrons, or features of meson decays and spectroscopy. In weak interactions we pursue questions, which are by definition more speculative and which go beyond the Standard Model of particle physics, particularly with regard to the nature of dark matter. We will confront theoretical predictions with direct searches for cold dark matter particles or for heavy neutrinos as well as with new particle searches at the LHC. The pillars of our qualification programme are individual supervision and mentoring by one senior experimentalist and one senior theorist, topical lectures in physics and related fields (e.g. advanced computation), peer-to-peer training through active participation in two research groups, dedicated training in soft skills, and the promotion of research experience in the international community. We envisage early career steps through a transfer of responsibilities and international visibility with stays at external partner institutions. An important goal of this Research Training Group is to train a new generation of scientists, who are not only successful specialists in their fields, but who have a broader training both in theoretical and experimental nuclear, particle and astroparticle physics. online • CRC 878 C04 - Mathematical aspects of QFT and condensed matter We continue our work on solvable quantum field theory models on noncommutative geometries and extend them to several components. In order to give a rigorous foundation to the fractional quantum Hall effect we work on a construction of a KK-element which classifies topological effects in disordered materials. Mathematische Aspekte von Quantenfeldtheorie und kondensierter Materie.online • EXC 2044 - B3: Operator algebras & mathematical physics The development of operator algebras was largely motivated by physics since they provide the right mathematical framework for quantum mechanics. Since then, operator algebras have turned into a subject of their own. We will pursue the many fascinating connections to (functional) analysis, algebra, topology, group theory and logic, and eventually connect back to mathematical physics via random matrices and non-commutative geometry. online• CRC 1442: Geometry: Deformation and Rigidity - D03: Integrability The project investigates a novel integrable system which arises from a quantum field theory on noncommutative geometry. It is characterised by a recursive system of equations with conjecturally rational solutions. The goal is to deduce their generating function and to relate the rational coefficients in the generating function to intersection numbers of tautological characteristic classes on some moduli space. online |

Project membershipMathematics Münster | B: Spaces and OperatorsB3: Operator algebras & mathematical physics C1: Evolution and asymptotics C3: Interacting particle systems and phase transitions |

Current Talks | • The Euclidean λφ^4_4-model on noncommutative geometries: a status report. Energy conditions in quantum field theory, Leipzig Slides Link to event• How topological recursion organises quantum fields on noncommutative geometries (3 lectures). Fields Institute Workshop on Noncommutative Geometry, Free Probability Theory and Random Matrix Theory, London (Ontario) Slides Link to event• Solution of the λΦ^4-matrix model. Random Geometry in Heidelberg, Heidelberg Slides Link to event• From scalar fields on noncommutative geometries to blobbed topological recursion. Emmy-Noether Seminar, Universität Leipzig, Deutschland Slides Link to event• On ‘Topological recursion, discrete surfaces and cohomological field theories’ by Elba Garcia-Failde. Higher Structures Emerging from Renormalisation, Erwin-Schrödinger-Institut, Vienna, Austria Slides Link to event• From scalar fields on noncommutative geometries to blobbed topological recursion. Workshop on Quantum Geometry, Field Theory and Gravity, Corfu, Greece Slides Link to event• From noncommutative field theory towards topological recurrence. Noncommutative Geometry and Physics, (remotely) Slides Link to event• Topological recursion of scalar fields in noncommutative geometry. The Noncommutative Geometry Seminar, (remotely) Slides Link to event• Blobbed topological recursion of the quartic analogue of the Kontsevich model. Research seminar "Structure of Local Quantum Field Theories", Humboldt-Universität zu Berlin, Berlin, Deutschland Slides Link to event |

Current Publications | • Branahl J, Grosse H, Hock A, Wulkenhaar R From scalar fields on quantum spaces to blobbed topological recursion. Vol. 2022, 2022 online• Schürmann J, Wulkenhaar R An algebraic approach to a quartic analogue of the Kontsevich model. Vol. 2022, 2022 online• de Jong J, Hock A, Wulkenhaar R Nested Catalan tables and a recurrence relation in noncommutative quantum field theory. Annales de l'Institut Henri Poincaré D Vol. 9 (1), 2022 online• Branahl J, Hock A, Wulkenhaar R Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures. Communications in Mathematical Physics Vol. 393, 2022 online• Branahl J, Hock A, Wulkenhaar R Perturbative and geometric analysis of the quartic Kontsevich model. SIGMA Vol. 17, 2021 online• Pascalie R, Pérez-Sánchez C I, Wulkenhaar R Correlation functions of U(N)-tensor models and their Schwinger-Dyson equations. Annales de l'Institut Henri Poincaré D Vol. 8 (3), 2021, pp 377-458 online• Hock Alexander; Wulkenhaar, Raimar Blobbed topological recursion of the quartic Kontsevich model II: Genus=0. , 2021 online• Grosse H, Hock A, Wulkenhaar R Solution of the self-dual \Phi^4 QFT-model on four-dimensional Moyal space. Journal of High Energy Physics Vol. 01, 2020, pp 081 online• Panzer E, Wulkenhaar R Lambert-W solves the noncommutative \Phi^4-model. Communications in Mathematical Physics Vol. 374, 2020, pp 1935-1961 online |

E-Mail | raimar at uni-muenster dot de |

Phone | +49 251 83-33734 |

Room | 416 |

Secretary | Sekretariat Dierkes Frau Gabi Dierkes Telefon +49 251 83-33730 Fax +49 251 83-32720 Zimmer 414 |

Address | Prof. Dr. Raimar Wulkenhaar Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |

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