Algebraic Geometry Seminar

There are many situations where one needs to assign finite values to integrals that diverge like log(x) near x=0 (the integral of 1/x). Such a "regularization" is typically achieved by expanding the integral in series, and discarding divergent terms, in a manner that depends on coordinates. I will explain a framework, based on logarithmic algebraic geometry, in which such regularized integrals are reinterpreted as the natural comparison isomorphism between Betti and de Rham cohomology. Applications include a new proof of formality of the little disks operad (following ideas of Beilinson and Vaintrob), and the construction of a motivic Galois action in deformation quantization.

This talk is based on joint work with Clément Dupont and Erik Panzer.