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 seminar on spectral flow
We will read the book on Spectral Flow by Doll, Schulz-Bales, Waterstraat, available as pdf here. References are to Chapters and Sections in this book.
| Date (Thursdays) | Room | Topic | Sections | Speaker |
| 6 November 2025 (14:00-15:00) | HG00.068 | Spectral flow in finite dimensions | 1.1-1.5 | Chris Pirie |
| 13 November 2025 (14:00-15:00) | HG00.068 | Spectral flow for bounded self-adjoint Fredholm operators | 3.6,4.1-4.3 | Luuk Venbrux |
| 20 November 2025 (14:00-15:00) | HG00.068 | Fredholm pairs and their index | 5.1-5.7 | Eline de Jager |
| 27 November 2025 (14:00-15:00) | HG00.068 | Spectral flow for unbounded self-adjoint Fredholm operators | 6.1-6.4, 7.1-7.2 | |
| 4 December 2025 (14:00-15:00) | HG00.068 | Index pairings and spectral localizer | 10.1-10.5 | Matt Verhoeven |
| 11 December 2025 (14:00-15:00) | HG00.068 | Homotopy theory of Fredholm operators | 8.1-8.4 | Cisca Kalmijn |
| 18 December 2025 (14:00-15:00) | HG00.068 | Spectral flow in semifinite von Neumann algebras | 11.1-11.6 | |
| 8 January 2026 (14:00-15:00) | HG00.086 | E-mergence of the spectral localizer ? | arxiv:2506.17143 | |
| 15 January 2026 (14:00-15:00) | HG00.086 | Spectral localizer in KK-theory ? | arXiv:2508.08668 | |
| 22 January 2026 (14:00-15:00) | HG00.086 | Applications to topological insulators ? | ||
| 29 January 2026 (14:00-15:00) |
Past reading seminars
In Spring 2025 we had a reading seminar on “foliations, groupoids and index theory”
| 6 March | 1.028 | (Regular) foliations, holonomy | MM, ch 1-2 | Enrico Maresca |
| 20 March | 00.310 | Lie groupoids, the holonomy groupoid | MM, ch 5 (especially 5.1 and 5.2), CFM13.1, 13.2 | Matthijs Lau |
| 10 April | 00.310 | Lie algebroids | MM, ch 6, CFM 13.3, 13.4 | Chris Pirie |
| 17 April | 2.032 | The C*-algebra of a groupoid | DL, 2.2 | Collin Joseph |
| 24 April | 00.310 | Deformation to the normal cone, Adiabatic groupoid | DS 2.3.1, 3.1.4, 3.3, DL 1.7 | Malte Leimbach |
| 15 May | 00.310 | Groupoid index | DS 3.1, 3.2, 3.3 (DL p53 is a KK-theory approach) MP, Tangent groupoid case: section II.5 of C94 | Thijs de Kok |
| 22 May | 00.310 | Cyclic cohomology | C94 (parts of) III.1-3 | Eline de Jager |
| 5 June | 00.310 | Index theorem for regular foliations | C94 III.7, C86 | Peter Hochs |
| 19 June | 00.310 | Androulidakis-Skandalis holonomy groupoid for singular foliations | AS | Florian Zeiser |
| ? | ? | Mohsen’s blowup groupoid for singular foliations | M | ? |
- MM: Moerdijk & Mrcun, Introduction to foliations and Lie groupoids
- CFM: Crainic, Fernandez, Marcut, Lectures on Poisson Geometry
- DS: Debord and Skandalis, Lie groupoids, pseudodifferential calculus, and index theory, Advances in noncommutative geometry—on the occasion of Alain Connes’ 70th birthday, 245–289, Springer, Cham, [2019], ArXiv:1907.05258
- DL: Debord & Lescure, Index theory and groupoids, Geometric and topological methods for quantum field theory, 86–158, Cambridge Univ. Press, Cambridge, 2010, ArXiv:0801.3617
- CS: Connes, A. (F-IHES); Skandalis, G. The longitudinal index theorem for foliations. Publ. Res. Inst. Math. Sci. 20 (1984), no. 6, 1139–1183.
- AS: Androulidakis and Skandalis, The holonomy groupoid of a singular foliation, J. Reine Angew. Math. 626 (2009), 1–37.
- M: Mohsen, Blow-up groupoid of singular foliations, arXiv:2105.05201
- MP: Monthubert and Pierrot, “Indice analytique et groupoïdes de Lie”, C.R. Acad. Sci. Paris 325, 1997
- C94: Connes, “Noncommutative geometry”, Academic Press, 1994
- C86: Connes, “Cyclic cohomology and the transverse fundamental class of a foliation”, Geometric methods in operator algebras (Kyoto, 1983), pp 55-144, Pitman Res Notes in Math 123, 1986
In Fall 2024 we had a reading 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.
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 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
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.