The weight 0 compactly supported Euler characteristic of moduli spaces of marked hyperelliptic curves

Joint work with Madeline Brandt and Siddarth Kannan.  We use moduli spaces of G-admissible covers and tropical geometry to give a sum-over-graphs formula for the weight-0 compactly supported Euler characteristic of the moduli spaces H_{g,n} of n-marked hyperelliptic curves of genus g, as a virtual representation of S_n.  Computer calculations then enable fully explicit formulas for the above in small genus.  My aim is to make this talk accessible to anyone with passing familiarity with M_g and its Deligne-Mumford compactification.