Recently, regularity issues have increasingly come into the focus of researchers in Mathematical General Relativity and in Lorentzian geometry as they have turned out to be crucial in solving some of the most persistent open questions in the field. Traditionally most studies have assumed, explicitly or implicitly, smoothness of the metric. However, new insights are needed when the metric is not $C^2$ and, consequently, it appears reasonable to call such geometries non-regular spacetimes.

In Riemannian signature geometers have long studied non-regular manifolds using a variety of methods, such as comparison geometry, metric geometry and others. Many of these techniques have yet to be exported to the Lorentzian setting since, of course, a number of difficulties have to be addressed. At the moment the field is very dynamic as new methods and approaches are being developed and merged together with older techniques and accounts.

This workshop aims at gathering researchers at the forefront of the field to discuss and advance recent related results in areas such as causality theory, cone and Lorentz-Finsler structures, Alexandrov geometry, length spaces, metric geometry, ${C}^0$-extendibility of spacetimes, transport theory and curvature-dimension conditions, as well as non-commutative geometry.