Abstract: Ancient flows arise as singularity models via blow-ups, and the first examples were found by Mullins in 1956. Insight from gluing constructions indicate that classifying them fully is not viable, except under e.g. pointwise positive curvature assumptions. However, without any such restrictions on curvatures or topology, if one applies certain "forgetful" operations - discard time coordinates and take convex hulls - then we show that only four types of behavior may occur. For this, we first prove a natural "wedge theorem" for proper ancient flows, which adds to a long story: F.ex. it generalizes our own wedge theorem for self-translaters from 2018 (the main motivating case in the talk) which implies the minimal surface case by Hoffman-Meeks from 1990 that in turn contains the classical cone theorem by Omori from 1967. This is joint work with Francesco Chini (U Copenhagen).