Michael Temkin of the Institute for Advanced Study presents a research seminar on Hurwitz moduli spaces of degree d covers of curves in the wild ramification case, where d! fails to be invertible. He opens with the Abramovich-Oort example, the schematic closure of the classical space H_{2,1,0,4} of double covers of P^1 branched at four points, computed over Z and found strange over F_2 but without a modular interpretation. Temkin then describes work in progress with Hippold constructing a logarithmic modular version of the degree p Hurwitz space when only (p-1)! is invertible, which explains the earlier phenomenon conceptually. The second half turns to a result of Abramovich-Olsson-Vistoli showing this space is a blow up of the modular curve X(2), and uses the same ideas to refine Drinfeld's wild level structures, aiming at modular interpretations of minimal modifications of X(p^n) that separate ordinary branches at supersingular points. The talk closes with open questions from this unfinished research.