Deformation Theory Seminar: Framed Formal Curves

Seminar | April 17 | 2:30-3:50 p.m. | Mathematical Sciences Research Institute, Baker Room

 Dmitry Vaintrob, UC Berkeley

 Department of Mathematics

I will talk about a new moduli-theoretic interpretation of the spaces of framed little disks, as well as their higher-genus generalization of complex curves with parametrized boundary, as geometric objects over the rational field Q. Applications of this formalism give geometric "explainations" for several results previously proven using transcendental or analytic methods, namely formality of $E_n$ operads, Galois action on Drinfeld associators, and certain relations between "modular" periods and zeta functions proven by Hain.