The moduli space of smooth curves with a chosen differential form has a natural stratification by the pattern of zeros of the form. In a recent paper of Bainbridge-Chen-Gendron-Grushevsky-Moeller, one used a complicated complex-analytic technique to explicitly describe a compactification of these strata. In a joint work in progress with I. Tyomkin we provide an algebraic proof of these results based on studying differential forms on Berkovich curves over fields of residual characteristic zero. In a series of two talks I will formulate the result of BCGGM as a motivation and will explain how our Berkovich analytic proof works. Probably the first talk will be mainly devoted to the result of BCGGM and an introduction to the theory of Berkovich curves, and our work will be described in the second talk.