Speaker: Siddharth Kannan (MIT)

Title: Radially aligned stable curves and applications

Abstract:

I will discuss a combinatorially defined blow-up of the moduli space of curves in genus g <= 1 and then describe two applications of this construction. The first application is more combinatorial: a modular understanding of the blow-up leads to a calculation scheme for the S_n-representations defined by the Chow ring of the braid matroid. The second application is more geometric: a combinatorial understanding of the boundary complex of the blow-up leads to a calculation of the weight zero subspace of the compactly-supported cohomology of the moduli space M_1,n(P^r, d), which parameterizes degree d maps from smooth pointed genus one curves to P^r. The talk will be based on separate joint projects, with Lukas Kühne and with Terry Song.