The double ramification cycle parametrizes algebraic curves (or Riemann surfaces) of genus g admitting maps to the projective line (or Riemann sphere) with specified branching over two points. I'll describe a formula giving the class of this cycle in the cohomology of the moduli space of curves. I'll then discuss some of the combinatorial features of this formula and how they relate back to geometry.
Speaker(s): Aaron Pixton (University of Michigan)