Speaker: Melody Chan (Brown University)

Title: A Hopf algebra in the cohomology of moduli of abelian varieties

Abstract: I will discuss aspects of joint work with Brown, Galatius, and Payne. In particular, we identify a Hopf algebraic structure in the weight 0 cohomology with compact supports of the moduli space of abelian varieties, and we deduce exponential growth results as a corollary. A key role is played by the moduli space of tropical abelian varieties, which is stratified by locally symmetric spaces GL_n(Z)_n(R)/O(n) . I will try to emphasize aspects of this work not discussed in Galatius' talk in this seminar.