主持人：骆文斌 研究员

报告简介：
The geometric average of a polynomial over the real unit torus is a way to measure the polynomial's complexity content, introduced by Mahler to study questions in transcendence theory. In this talk, we will see how this quantity, and its p-adic analogues, are related to heights in Diophantine geometry, entropies of dynamical systems, and growth rates of invariants associated to towers of knots and graphs, which are reminiscent of classical formulas in Iwasawa theory. Moreover, we will see how the study of small, univariate Mahler measures leads naturally to the study of multivariate ones, which are conjecturally connected to special values of L-functions. This is based on joint works with Fran?ois Brunault, Antonin Guilloux, Mahya Mehrabdollahei and Daniel Vallières.

主讲人简介：
Riccardo Pengo, 意大利Messina大学研究员，主要研究方向涉及数论与算术几何。2012