# School

The academic program consists of a 3-day graduate school and a 2-day conference.

### Graduate School (June 4 to 8, 2018)

The idea behind the GQT school is that participants will get a basic understanding of some central topics in GQT-research, including many important themes which may lie outside one’s own research specialization. Hence, we strongly encourage Ph.D. students to participate in all three days as a way to broaden their mathematical formation and increase awareness regarding the research carried out within the cluster.

Another important side to the event is that it will provide the opportunity for graduate students within the GQT to get to know and socialize with each other as well as have some academic interaction.

The school will consist of three days of lectures and exercise sessions; the topics and speakers are as follows:

- June 4 — Gil Cavalcanti (UU): Generalized complex geometry
- June 5 — Walter van Suijlekom (Nijmegen): Non-commutative geometry
- June 6 — Hessel Posthuma (UvA): Index theory

Besides the three minicourses, there will be one or two Ph.D. talks (given by Ph.D. students to Ph.D. students) on Tuesday and Wednesday morning before the beginning of the minicourse.

**Schedule**

During the school days the lectures and exercise classes will be arranged roughly as follows:

Mon | Tue | Wed | |
---|---|---|---|

9:00 – 10:00 | Arrival | Speaker 1 | Speaker 2 |

10:00 – 11:00 | Lecture | Lecture | Lecture |

11:00 – 12:00 | Lecture | Lecture | Lecture |

12:00 – 12:30 | Discussion | Discussion | Discussion |

12:30 – 14:00 | Lunch | Lunch | Lunch |

14:00 – 15:00 | Lecture | Lecture | Lecture |

15:00 – 16:00 | Lecture | Lecture | Lecture |

16:00 – 17:00 | Exercises | Exercises | Exercises |

17:00 – 18:00 | Exercises | Exercises | Exercises |

18:00 – 19:00 | Solution of exercises | Solution of exercises | Solution of exercises |

19:00 | Dinner | Dinner | Dinner |

**Course description and prerequisites**

**Generalized complex geometry** — Gil Cavalcanti (UU)

*Course description*: TBA.

*Pre-requisites*: TBA.

*Reading material*: TBA.

**Index theory** — Hessel Posthuma (UvA)

*Course description*: TBA

*Pre-requisites*: TBA

*Reading material*: TBA

**Non-commutative geometry** — Walter van Suijlekom (Nijmegen)

*Course description*: We will start the morning sessions by presenting a “light” version of noncommutative geometry by looking at finite noncommutative metric spaces (aka finite spectral triples) and their classification. We discuss bimodules and Morita equivalences in this context, and explain how to take a “product” of a finite spectral triple and a Morita equivalence bimodule to obtain a new finite spectral triple.

We will then move on to the general notion of KK-cycles and introduce the key structure given by the interior Kasparov product, of which the above product with a Morita bimodule is an example. We will avoid all functional analytical technicalities by working in the finite-dimensional case, even though towards the end we will briefly sketch how to extend the formalism to that case. This will be illustrated by concrete geometric examples coming from gauge theory and index theory.

* Pre-requisites*: Some Hilbert space theory, differential geometry.

*Reading material*: W.D. van Suijlekom. Noncommutative Geometry and Particle Physics. Springer, 2015 (a draft is available at www.waltervansuijlekom.nl).

Ph.D. talks

TBA