- 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 2022 spring semester, we ran a reading seminar on K-theory and KK-theory at Leiden university. In this seminar we studied some basic knowledge of KK-theory for C*-algebras. We began with a quick recap of the properties of K-theory, focusing on its formal properties like the Bott periodicity and Thom isomorphisms, which became more illuminating in the framework of KK-theory. Then we provided the two basic pictures of KK-theory due to Kasparov and Cuntz. After that we studied the formal properties of KK-theory, which are mostly due to the existence of the Kasparov product. Using the Kasparov product we are able to construct a category KK which is equipped with a triangulated structure, so various toolkits from homological algebra can be adapted to it. In the end, we discussed the unbounded picture of KK-theory, whose theory had been developed rapidly in recent years and proved to be useful in the study of noncommutative differential geometry.

**Prerequisites**. The participants should be familiar with basic theory of C*-algebras. Knowledge on the K-theory of C*-algebras is not assumed but suggested.

Bram Mesland, Jack Ekenstam, Yufan Ge and Yuezhao Li. If you are interested: please contact Yuezhao Li (y.li AT math.leidenuniv.nl).

**Tuesdays, 12.15-14.00, in Gorlaeus building**.

Notes of the talks are available here.

Date | Location | Speaker | Title |
---|---|---|---|

Feb 15 | Gorlaeus DM017PC | Jack Ekenstam | K-theory of C*-algebras 1 |

Feb 22 | Gorlaeus DM017PC | Yuezhao Li | K-theory of C*-algebras 2 |

Mar 1 | Gorlaeus DM009PC |
Jack Ekenstam | Hilbert C*-modules 1 |

Mar 8 | Gorlaeus DM017PC | Jack Ekenstam, Yufan Ge | Hilbert C*-modules 2, Kasparov’s picture of KK-theory 1 |

Mar 15 | — | — | No talk |

Mar 22 | Gorlaeus DM017PC | Yufan Ge | Kasparov’s picture of KK-theory 2 |

Mar 29 | Gorlaeus DM109 |
Yufan Ge | Cuntz’s picture of KK-theory |

Apr 5 | Gorlaeus DM017PC | Yuezhao Li | Examples and properties of KK-theory |

Apr 12 | Gorlaeus DM017PC | Bram Mesland | The Kasparov product 1 |

Apr 19 | Gorlaeus DM017PC | Bram Mesland | The Kasparov product 2 |

Apr 26 | — | — | No talk |

May 3 | Gorlaeus DM017PC | Georg Huppertz | Extension of C*-algebras and KK-theory 1 |

May 10 | Gorlaeus DM017PC | Georg Huppertz, Yuezhao Li | Extension of C*-algebras and KK-theory 2, Categorical aspect of KK-theory 1 |

May 17 | Gorlaeus DM017PC | Yuezhao Li | Categorical aspect of KK-theory 2 |

May 24 | Gorlaeus DM017PC | Dimitris Gerontogiannis | Finite summability in K-homology |

May 31 | — | — | No talk (due to Noncommutative Geometry Along the North Sea 2022) |

Jun 7 | Gorlaeus DM017PC | Mick Gielen | E-theory |

Jun 14 | Gorlaeus DM017PC | Yufan Ge | K-theory of graph C*-algebras |

Jun 21 | Gorlaeus DM017PC | Francesca Arici | K-theory of Cuntz-Pimsner algebras |