Margarida Melo: The tropicalization of the moduli space of stable spin curves

Abstract: The theory of linear series on tropical curves allows for a combinatorial systematic treatment of degenerations of classical linear series, leading to a number of beautiful results connecting classical and tropical viewpoints. The moduli space of spin curves over curves of given genus and its compactification by Cornalba are very well studied spaces and, jointly with their generalized version for moduli of higher roots, are important tools in the understanding of the moduli space of curves itself. Building on the beautiful framework developed by Abramovich, Caporaso and Payne on the relation between the analytification and the tropicalization of the moduli space of curves, I will report on ongoing joint work with Lucia Caporaso and Marco Pacini describing the tropicalization of Cornalba's space and relating this with the moduli space of tropical spin curves.