Many of the classical concepts in representation theory, such as torsion classes and tilting theory, have generalisations to higher homological algebra, where the role of short exact sequences is played by exact sequences of longer length. In this talk, we explore the connection between $n$-torsion classes and $\tau_n$-tilting theory (where $n=1$ is the classical setup).

This is joint work with J. Haugland, K. Jacobsen, S. Kvamme, Y. Palu and H. Treffinger.