Matilde Lalin
Title: Mahler measures and regulators
Abstract:
The Mahler measure of an n-variable polynomial P is the integral
of log|P| over the n-dimensional unit torus T^n with the Haar
measure. For one-variable polynomials, this is a natural quantity
that appears in different problems such as Lehmer's question.
While the algebraic nature of the values of the Mahler measure for
one-variable polynomials with integral coefficients is well
understood, the knowledge of the several-variable case is reduced to
a collection of examples, some of which are related to special
values of L-functions and/or polylogarithms. This phenomenon may be
explained in terms of evaluations of regulators. In turn, regulators
also allow us to prove new formulas for Mahler measures involving
genus-one curves.