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

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.

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

28 Feb 2024: **Dimitris Gerontogiannis** (Leiden)

**Title**: TBA

**Abstract**: TBA

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

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.

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**.