Artin fans, piecewise polynomials and the double ramification cycle

Date: 2021-11-15

Time: 09:45 - 10:45

Zoom link:


Samouil Molcho


The double ramification cycle — roughly, the locus of curves admitting a rational function with given ramification over 0 and infinity — is a cycle class on the moduli space of curves, with connections to both Gromov-Witten theory and Abel-Jacobi theory. Some years ago, a remarkable formula for the DR cycle in terms of tautological classes was conjectured by Pixton, and subsequently proven in work of Janda, Pandharipande, Pixton and Zvonkine. However, in order to make further progress in this line of study — for instance, in order to study the Gromov-Witten theory of more complicated targets — it is necessary to study a refinement of the DR cycle coming from logarithmic geometry, for which no formulas exist. In the talk, I want to explain the key tools that, in joint work with Holmes,Pandharipande, Pixton and Schmitt, allow us to obtain such formulas. The moduli space of tropical curves, the cohomology rings of certain algebraic stacks and the compactified Jacobians of Kass-Pagani will play a crucial role.