Title: Operads, motives and logarithmic geometry
Speaker: Dmitry Vaintrob
Speaker Info: UC Berkeley
The category of (differential graded) Gerstenhaber algebras is known to have a rich and mysterious group of so-called "motivic" symmetries. These symmetries, discovered by Dmitry Tamarkin, follow from a connection between Drinfeld associators and the operad Gerst classifying operations in the Gerstenhaber algebra, and imply several important formality and rigidity results including Kontsevich's deformation quantization theorem, that any Poisson manifold admits a quantization.Date: Thursday, December 05, 2019
I will talk about a new point of view on these symmetries, using a geometric model expressing the operad Gerst in terms of an operad in logarithmic algebraic geometry, with Betti realization the operad of little disks. This point of view implies an "integral-less" proof of several algebraic results previously proven using analytic inputs, including deformation-quantization. I will explain a generalization of this point of view to the operad BV responsible for BV algebras, as well as higher-genus analogues.