Multivariable Mahler Measure and Regulators

MEMBERS SEMINAR
Topic:Multivariable Mahler Measure and Regulators
Speaker:Matilde Lalin
Affiliation:IAS
Date:Monday, March 13
Time/Room:4:00pm - 5:00pm/S-101

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 have been interpreted in terms of values of regulators.