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NCG-Leiden

Seminars

2024 spring
- Research seminar
2023 fall
- Foliations
2022 fall
- Groupoid C*-algebras
2022 spring
- K(K)-Theory
2021 fall
- Deformation Quantization and Index Theory


Workshops

2023 spring
- Geometry and Operator ALgebras 2023
2022 fall
- NCG Day 2022

Noncommutative Geometry Research Seminar

2024 spring semester

In 2024 spring semester, the noncommutative geometry group of Leiden university is running a local NCG research seminar on Wednesdays from 15:15-16:15. If you want to be added to the mailing list for this seminar, please contact Francesca Arici or Bram Mesland.

Date and time

Wednesdays, 15:15-16:15. Room: DM 1.15 or DM 1.19, as indicated below.


Upcoming talks

28 Feb 2024: Dimitris Gerontogiannis (Leiden)

Title: TBA

Abstract: TBA

Place and time: DM 1.15. 15:15-16:15.


Room schedule

From 07 Feb to 27 Mar, we will be in Gorlaeus Gebouw DM 1.15, except for March 13th, when we will be in DM 1.19.

From 03 Apr onwards, we will be in Gorlaeus Gebouw DM 1.19.


Previous talks

21 Feb 2024: Sophie Zegers (Delft)

Title: Split extensions and KK-equivalences for quantum flag manifolds

Abstract: In this talk, I will first present the explicit KK-equivalence between $C(\mathbb{C}P_q^n)$ and the commutative algebra $\mathbb{C}^{n+1}$ constructed in collaboration with Francesca Arici. The KK-equivalence is constructed by finding an explicit splitting for the short exact sequence $\mathcal{K}\to C(\mathbb{C}P_q^n)\to C(\mathbb{C}P_q^{n-1})$. In the construction of a splitting it is crucial that $C(\mathbb{C}P_q^n)$ can be described as a graph algebra. Secondly, I will present how this approach can be used to construct KK-equivalences in the more general framework of quantum flag manifolds which is based on ongoing work with Réamonn Ó Buachalla and Karen Strung.

Place and time: DM 1.15. 15:15-16:15.


14 Feb 2024: Yufan Ge (Leiden)

Title: SU(2)-symmetries of C*-algebras: from bricks to buildings

Abstract: In this talk, we will consider subproduct systems coming from SU(2)-representations and discuss the associated C*-algebras. We will first review results concerning irreducible representations from Arici–Kaad, then provide some further results about more general cases. More specifically, we will discuss the structure of the SU(2)- subproduct systems associated to isotypic representations and multiplicity-free representations. Finally, we will provide results about the K-theory groups of their Toeplitz algebras. This is joint work in progress with Francesca Arici.

Place and time: DM 1.15. 15:15-16:15.


7 Feb 2024: Adam Rennie (Wollongong)

Title: Using the Cayley transform to relate van Daele K-theory and KK

Abstract: I will start with a warm-up in the (friendly) complex case showing that $K_1(A)\cong KK^1(\mathbb{C},A)$ via the Cayley transform. Then I will show that the “same” thing works in real, Real, graded cases when we start with van Daele K-theory. This will involve some discussion of van Daele K-theory, and how one defines it…which is slightly intricate.

Why did we want to do all that? Make Kasparov products easy of course!!

Joint work with Chris Bourne and Johannes Kellendonk.

Place and time: DM 1.15. 15:15-16:15.


24 Jan 2024: Francesca Arici (Leiden)

Title: Some results about the K-theory of C*-algebras of subproduct systems

Abstract: In this talk, we will consider subproduct systems of Hilbert spaces and their Toeplitz and Cuntz–Pimsner algebras, and discuss their relation to the theory of polynomials in noncommuting variables. We will provide results about their topological invariants through K(K)-theory and discuss some open problems.

Place and time: DM 1.19. 15:30-16:30.