Short talk: Motivic Mahler measures and Eisenstein series

Mahler measures of polynomials have been known to be periods of Deligne cohomology since the seminal work of Deninger. This explains some links between Mahler measures and special values of L-functions, which were observed by Boyd and Rodriguez-Villegas, and proven in some cases using the method of Rogers and Zudilin, which allows one to perform explicit regulator computations using Eisenstein series. In this talk, based on a joint work in progress with François Brunault, I will outline a general construction which exhibits the Mahler measure as a mixed period, and allows to explain motivically more relations between Mahler measures and special values of L-functions. If time permits, we will briefly talk about possible generalizations of the Rogers-Zudilin method to this setting.