This is an informal seminar on noncommutative geometry and related topics organized by the group of master students, PhD students, postdocs and staff working on topics related to noncommutative geometry in Nijmegen and its surroundings. At the same time, it forms a platform where we share with each other our ideas, projects, problems, papers, etc.

**Schedule*** Reading mini-seminar on “modular theory and entropy”* (as a preparation to this mini-course on modular theory in Utrecht)

Wednesday October 16, 2024 (14:00, HG02.802) | More on modular theory and entropy) | Selected topics from [Rei, IV, V], [BR2, 6.2.3] | ||

Wednesday October 9, 2024 (14:00, HG02.802) | Modular theory II | [Rei, III], [BR1, 2.5], [Bla III.4] | “time emergence”, Radon-Nykodim theorem for weights | |

Wednesday October 2, 2024 (14:00, HG02.802) | Silvester Borsboom | Modular theory I | [Rei, III], [BR1, 2.5], [Bla III.4] | Modular group, Tomita–Takesaki theorem, weights, KMS condition, |

Wednesday September 25, 2024 (14:00, HG02.802) | Jort de Groot | Classification of factors and relative entropy when it seems hopeless | Bla; III.1, III.3 and III.4] , and 1803.04993 | (Lattice of) projections, factors, types, dimension, direct integral |

Wednesday September 18, 2024 (14:00, HG02.802) | Walter van Suijlekom | Introduction to entropy | [BR1,2] | Density matrices, von Neumann entropy, examples, inequalities |

Wednesday September 11, 2024 (14:00, HG02.802) | Malte Leimbach | Basics of von Neumann algebras | [Rei, II.3, II.4.b,c], [BR1, 2.4] | Operator topologies, bicommutant theorem, density theorems, normal functionals and preduals, W*-algebras, tensor products |

[Bla] B. Blackadar, Theory of operator algebras.

[BR1] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1.

[BR2] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 2.

[Rei] B. M. Reible, Monotonicity of the Relative Entropy and the Two-sided Bogoliubov Inequality in von Neumann Algebras, Master’s thesis.

[Tak1] M. Takesaki, Theory of operator algebras I.

**Past seminars**

Wednesday June 19, 2024 (14:00, HG00.308). *Eva-Maria Hekkelman (UNSW). *Functional calculus for pseudodifferential operators

Wednesday December 13, 2023 (14:00, HG02.802). *Fabian Lux* (Yeshiva University). From magnetic skyrmions to noncommutative geometry.

Wednesday December 6, 2023 (14:00, HG02.802). *Rodrigo Baptista*. Dirac geometry: local structure

Wednesday November 29, 2023 (14:00, HG00.514). *Collin Joseph. *Topological insulators.

Wednesday November 22, 2023 (14:00, HG00.616). *Rodrigo Baptista*. Dirac geometry: an introduction

Wednesday November 15, 2023 (14:00, HG02.802). *Gaston Nieuviarts (Genova University). *Spectral triple-based Noncommutative Gauge Field Theories on AF-algebras:

Wednesday November 8, 2023 (14:00, HG02.802). *Shane Farnsworth* (The Max Planck Institute for Gravitational Physics). Nonassociative spectral geometry.

Wednesday October 18, 2023 (14:00, HG03.082).* Malte Leimbach.* A von Neumann algebra approach to quantum metric spaces

Wednesday October 4, 2023 (14:00, HG02.802). *Luuk Verhoeven.* Random fuzzy geometries and their random matrix models

Wednesday September 27, 2023 (14:00, HG02.802). *Luuk Verhoeven. *Codimension one immersions as unbounded Kasparov products

Wednesday September 13, 2023 (14:00, HG00.308). *Eva-Maria Hekkelman. *The joy of MOIs: unbounded multiple operator integrals in NCG

**Past reading seminar**

In spring 2023 we have been reading the book on **higher index theory** by Rufus Willett and Guoliang Yu (available online here):

Wednesday 5/7, (14:00, HG02.802) | Collin Joseph | Application: positive curvature | W&Y 10.2 |

Wednesday 21/6, (14:00, HG00.308) | Malte Leimbach | Controlled/quantitative K-theory | |

Wednesday 7/6, (14:00, HG02.508) | Yufan Ge | Equivariant Roe algebras and their relation to group C* algebras | W&Y 5.2-5.3 |

Wednesday 24/5, (14:00, HG02.508) | Aquerman Kuczmenda Yanes | Higher index via D*-algebras | Papers by Roe |

Wednesday 19/4, (14:00, HG02.508) | Yuezhao Li | Localization algebras | W&Y 6 |

Wednesday 5/4, (14:00, HG02.508) | Simon Pepin Lehalleur | The index as a pairing between K-theory and K-homology | Nigel Higson, John Roe. Analytic K-homology Ch. 8.7 |

Wednesday 29/3, (14:00, HG03.054) | Peter Hochs | Elliptic operators and Dirac type operators connections to K-homology | Nigel Higson, John Roe. Analytic K-homology Ch. 10 |

Wednesday 15/3, (14:00, | Yufan Ge | K-homology | Nigel Higson, John Roe. Analytic K-homology Ch. 8.1-8.3 |

Wednesday 1/3, (14:00, HG03.054) | Maxime Wybouw | Coarse geometry | Nigel Higson, John Roe. Analytic K-homology Ch. 6 / J. Roe. Lectures on coarse geometry |

Wednesday 22/2, (14:00, HG03.054) | Malte Leimbach | Roe algebras | W&Y: Sect 4.1-4.3, 5.1 |

Wednesday 15/2, (14:00, HG03.054) | Collin Joseph | K-theory for C*-algebras II | W&Y: Ch2 |

Wednesday 8/2, (14:00, HG03.054) | Aquerman Kuczmenda Yanes | K-theory for C*-algebras I | W&Y: Ch2 |

Wednesday 1/2, (14:00, HG03.054). | Walter van Suijlekom | Prelude to higher index theory and planning. | W&Y: Ch.3 |

**Past seminars **

Wednesday November 30, 2022 (14:00, room HG02.802). * Aquerman Kuczmenda Yanes* and

*Malte Leimbach*

Wednesday November 23, 2022 (14:00, room HG02.802). *Walter van Suijlekom – Planning for coming months*

Wednesday November 9, 2022 (14:00, room HFML0220). *Shintaro Nishikawa* *– K-theory of noncommutative Bernoulli Shifts*

Wednesday July 6, 2022 (14:00, room tba). *Aquerman Kuczmenda Yanes*

Wednesday June 15, 2022 (14:00, room HG02.052). *Peter Hochs –* *Analytic torsion*

Wednesday June 8, 2022 (14:00, room HG00.218). *Klaas Landsman – canceled*

Wednesday May 25, 2022 (14:00, room HG00.218). *Mick Gielen – Cyclic cohomology and generalized formal degrees for affine Hecke algebras*

Wednesday May 11, 2022 (14:00, room HG00.218). *Malte Leimbach – Spectral truncations of the torus*

Wednesday April 13, 2022 (14:00, room HG00.071). *Rui Dong – The gauge group and perturbation semigroup of an operator system*

Wednesday February 16, 2022 (14:00, room HG00.062). *Walter van Suijlekom – Noncommutative spaces at finite resolution [slides]*

Wednesday February 2, 2022 (14:00, room HG00.218). *Walter van Suijlekom – Planning for coming semester*

Wednesday March 18, 2020 (14:30, room tba). *Teun van Nuland – canceled (COVID-19).*

Tuesday February 4, 2020 (**Geometry Seminar**). *Saskia Roos (Potsdam)*

Tuesday January 28, 2020 (**Geometry Seminar**). *Michael Borinsky (NIKHEF)*

Tuesday January 14, 2020 (HG03.085). *Rui Dong – Fock space and second quantization.*

Tuesday January 7, 2020 (HG02.028).* Yari Kraak – Canonical quantization of free fields II.*

Tuesday December 10, 2019 (HG02.028). *Yari Kraak – Canonical quantization of free fields I.*

Tuesday November 26, 2019 (HG02.028). *Oscar de Wit – Lagrangian and Hamiltonian formalism: quantum mechanics. *

Tuesday November 12, 2019 (HG02.028). *Oscar de Wit – Lagrangian and Hamiltonian formalism: classical mechanics.*

Tuesday October 22, 2019. *Rui Dong – Spectral action and the second quantization.*

Tuesday May 7, 2019. *Debashish Singh** – Extracting Lorentzian structure from Euclidean fermionic action in noncommutative geometry.*

Tuesday April 9, 2019. *Ali Chamseddine – Mimetic Gravity and Dark Matter *(in **HG00.108**).

Tuesday April 2, 2019. *Ali Chamseddine – Noncommutative Geometry and Particle Physics: Unification *(in **HG00.622**).

Tuesday March 26, 2019. *Ali Chamseddine – Noncommutative Geometry and Particle Physics: Introduction *(in **HG00.622**, reception afterwards).

Tuesday March 19, 2019. *Luuk Verhoeven – Embedding the circle in the plane in unbounded KK-theory II.*

Tuesday March 12, 2019. *Luuk Verhoeven – Embedding the circle in the plane in unbounded KK-theory I.*

Tuesday February 26, 2019. *Walter van Suijlekom – Spectral triples and Gromov-Hausdorff convergence.*

Tuesday January 22, 2019. *John Barrett – Fuzzy non-commutative geometries.*

Tuesday January 15, 2019 *Luuk Verhoeven – Embedding the circle in the plane *(final presentation MSc thesis, in **HG00.068**)

Tuesday December 18, 2018. *Nesta van der Schaaf – Lie groupoids*

Tuesday December 4, 2018. *Nesta van der Schaaf – Lie groupoids*

Tuesday November 13, 2018. *Abel Stern – K-homology*

Tuesday November 6, 2018. *Abel Stern – K-theory*

Tuesday October 30, 2018. *Lisa Glaser – Simulating random non-commutative geometries.*

Tuesday October 23, 2018. *Tey Berendschot – Connes’ distance formula in noncommutative geometry. *

Tuesday October 16, 2018. *Luuk Verhoeven – Hearing the shape of a drum.*

Tuesday October 2, 2018. *Walter van Suijlekom – Dirac operators and spectral triples.*