Meeting ID:  920 2195 5230  Passcode:    The three-digit integer that is the cube of the sum of its digits. 

Orbits of many coregular representations of algebraic groups are closely linked to moduli spaces of genus one curves with extra data. We may use these orbit parametrizations to compute the average size of Selmer groups of elliptic curves in certain families, e.g., with marked points, thus obtaining upper bounds for the average ranks of the elliptic curves in these families. We will also describe some other applications. This is joint work with Manjul Bhargava. This first talk of the doubleheader will describe one orbit parametrization that will appear in the second talk by Ari Shnidman, but the two talks may be understood individually.