Relative Calabi-Yau completions and higher preprojective algebras

In this talk, we will give an introduction to (relative) Calabi-Yau structures following Brav-Dyckerhoff and (relative) Calabi-Yau completions following Yeung. We will then illustrate the relevance of these constructions to higher Auslander-Reiten theory on the example of higher preprojective algebras in the sense of Iyama-Oppermann. This is a report on part of Yilin Wu’s ongoing Ph. D. thesis.