Non-commutative geometry is an arsenal of tools to study non-commutative operator algebras from a topological or geometric viewpoint. Universal methods permit to treat ordinary Riemannian manifolds, spaces of non-integral dimensions (e.g. fractals and boundaries of trees) as well as spaces of leaves of a foliation and quantum groups on the same footing, using spectral triples. A finite set of points can be equipped into an interesting differential geometry where the spectral triple is represented by matrices, and studying random geometries then relates to random matrix models. Free probability and more generally non-commutative probability provide tools to study coupled systems of random matrices in the large size limit.
Topological recursion is a universal structure invented by Chekhov, Eynard and Orantin, providing a recursive procedure to compute all-order asymptotic expansions (for large size) in certain matrix models. Once formulated abstractly in terms of the geometry of spectral curves, it has found an increasing number of applications beyond matrix models: in enumerative geometry, mirror symmetry, low-dimensional quantum field theories, and more recently deformation quantization and hyperbolic geometry. Tropical geometry is an array of techniques to reduce problems of enumerative geometry to combinatorics.
Some promising bridges between these topics have been discovered in the last 5 years. This workshop therefore aims at developing further these interactions and encourage the transfer of knowledge to address problems in all four areas thanks to this broader perspective.© by Raimar Wulkenhaar
- Lecture 1
- Lecture 1
This session will take place in the Schrödinger Lecture Hall.
- Lecture 2
- Lecture 2
- Lecture 1
- Lecture 3
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 3
- Lecture 2
- Lecture 3
Organizers
Name | Affiliation |
---|---|
Gaëtan Borot | Humboldt University |
Elba Garcia Failde | Sorbonne University |
Harald Grosse | University of Vienna |
Masoud Khalkhali | Western University, Ontario |
Hannah Markwig | University of Tübingen |
Raimar Wulkenhaar | University of Münster |
Attendees
Name | Affiliation |
---|---|
Adam Afandi | University of Münster |
Omid Amini | Ecole Polytechnique, Palaiseau |
John Barrett | University of Nottingham |
Valentin Bonzom | University Paris-Nord |
Thomas Buc-d'Alche | Unité de Mathématiques Pures et Appliquées ENS Lyon |
Boris Bychkov | University of Haifa |
Ariane Carrance | Ecole Polytechnique, Palaiseau |
Renzo Cavalieri | Colorado State University |
Adrian Celestino Rodriguez | Technische Universität Graz |
Séverin Charbonnier | University of Genève |
Nitin Chidambaram | University of Edinburgh |
Alessandro Chiodo | Sorbonne University |
Benoit Collins | Kyoto University |
Kurusch Ebrahimi-Fard | Norwegian University for Science and Technology |
Maria Immaculada Gálvez Carrillo | Universitat Politecnica de Catalunya |
David García Zelada | Sorbonne University |
L Glaser | University of Vienna |
Marvin Anas Hahn | Trinity College |
Katharina Harengel | University of Münster |
Alexander Hock | University of Oxford |
Rei Inoue | Chiba University |
Roberta Anna Iseppi | Georg-August-Universität |
Finn Bjarne Kohl | University of Münster |
Thomas Krajewski | University Aix-Marseille |
Felix Leid | University of Saarland |
Luca Lionni | Heidelberg University |
Margarida Melo | University Roma Tre |
James Mingo | Queen's University |
Carlos Pérez Sánchez | University of Heidelberg |
Akifumi Sako | Tokyo University of Science |
Davide Scazzuso | Humboldt University |
Jörg Schürmann | University of Münster |
Sergey Shadrin | University of Amsterdam |
Roland Speicher | University of Saarland |
Teun van Nuland | University of New South Wales, Sydney |
Yannic Vargas | CUNEF University |