Seminar in Algebraic Geometry and Number Theory

Abstract: By considering variations of the uniformising differential equation of a genus 0 modular curve, Bogo defines a notion of a deformation of a modular form in terms of iterated integrals of modular forms, whose first order transformation properties are given in terms of period polynomials.

In this talk, we will provide a cohomological formalism for such deformations, establish the existence and near uniqueness of such deformations, and give an explicit example in terms of both critical and non critical totally holomorphic multiple L values, establishing a geometric interpretation for non-critical multiple L-values.