Non-commutative Geometry meets Topological Recursion

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

April 24, 2023
09:00 — 09:30
Registration & Welcome
09:30 — 10:30
10:30 — 11:00
Coffee Break
11:00 — 12:00
12:15 — 14:00
Lunch break
14:45 — 15:00
Coffee break
15:00 — 16:00
Gong talks 1
15:01 — 15:10
15:10 — 15:20
Thomas Buc-d'Alche (UMPA ENS Lyon)
Topological expansion of unitary integrals and maps
15:20 — 15:30
Adrian Celestino Rodriguez (TU Graz)
Cumulants in Non-commutative Probability and Hopf Algebras
15:30 — 15:40
15:40 — 15:50
L Glaser (U of Vienna)
Pictures of deformed spheres
15:50 — 16:00
Marvin Anas Hahn (Trinity College, Dublin)
Combinatorics of pruned Hurwitz numbers
16:00 — 16:15
Break
16:15 — 17:30
Gong talks 2

This session will take place in the Schrödinger Lecture Hall.

16:25 — 16:35
16:35 — 16:45
16:55 — 17:05
Carlos Pérez Sánchez (U Heidelberg)
(More on) gauge networks in noncommutative geometry
17:05 — 17:15
Davide Scazzuso (HU Berlin)
Strings and recursion
17:15 — 17:25
April 25, 2023
09:00 — 10:00
10:00 — 10:30
Coffee break
11:30 — 11:45
Break
11:45 — 12:30
12:30 — 14:30
Lunch break
14:30 — 15:30
15:30 — 15:45
Coffee break
15:45 — 16:45
April 26, 2023
09:00 — 10:00
10:00 — 10:30
Coffee break
10:30 — 11:30
11:30 — 11:45
Break
11:45 — 12:30
Valentin Bonzom (U Paris-Nord)
Enumeration of maps via integrability
18:30 — 22:00
Workshop Dinner
April 27, 2023
09:00 — 10:00
10:00 — 10:30
Coffee break
11:30 — 11:45
Break
12:30 — 14:15
Lunch break
14:15 — 15:15
15:15 — 15:45
Coffee break
April 28, 2023
09:00 — 10:00
10:00 — 10:30
Coffee break
11:15 — 12:00
12:00 — 12:15
Break
12:15 — 13:00
Maria Immaculada Gálvez Carrillo (UPC, Barcelona)
On B∞-algebra structures

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 Technical University of Graz
Preview of Alexander Hock - x-y symplectic transformation in topological recursion - Lecture 1
Alexander Hock (U Oxford): x-y symplectic transformation in topological recursion
April 24, 2023 09:30 — 10:30
Preview of Renzo Cavalieri - Tropical contributions to enumerative geometry of target dimension one - Lecture 1
Renzo Cavalieri (CSU, Fort Collins): Tropical contributions to enumerative geometry of target dimension one.
April 24, 2023 11:00 — 12:00
Preview of Renzo Cavalieri - Tropical contributions to enumerative geometry of target dimension one - Lecture 2
Renzo Cavalieri (CSU, Fort Collins): Tropical contributions to enumerative geometry of target dimension one
April 25, 2023 09:00 — 10:00
Preview of Omid Amini - Higher rank Voronoi decompositions and metric degenerations of tori
Omid Amini (École Polytechnique, Palaiseau): Higher rank Voronoi tilings and metric degenerations of tori
April 25, 2023 11:45 — 12:30
Preview of Renzo Cavalieri - Tropical contributions to enumerative geometry of target dimension one - Lecture 3
Renzo Cavalieri (CSU, Fort Collins): Tropical contributions to enumerative geometry of target dimension one
April 25, 2023 15:45 — 16:45
Preview of Valentin Bonzom - Enumeration of maps via integrability
Valentin Bonzom (U Paris-Nord): Enumeration of maps via integrability
April 26, 2023 11:45 — 12:30
Preview of Ariane Carrance - Exploring boundary conditions of bicolored maps: universal behaviors and new structures
Ariane Carrance (École Polytechnique, Palaiseau): Exploring boundary conditions of bicolored maps: universal behaviors and new structures
April 28, 2023 11:15 — 12:00
Preview of Maria Immaculada Gálvez Carrillo - On B∞-algebra structures
Maria Immaculada Gálvez Carrillo (UPC, Barcelona): On B∞-algebra structures
April 28, 2023 12:15 — 13:00
At a glance
Type:
Workshop
When:
April 24, 2023 — April 28, 2023
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Gaëtan Borot (HU Berlin)
Elba Garcia Failde (Sorbonne U, Paris)
Harald Grosse (U of Vienna)
Masoud Khalkhali (Western U, Ontario)
Hannah Markwig (U Tübingen)
Raimar Wulkenhaar (U Münster)