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。2012–2015 年在意大利米兰大学完成数学本科学习；2015–2017 年通过 ALGANT 项目在米兰大学与荷兰莱顿大学获得硕士学位，师从 Peter Bruin；2017–2020 年在丹麦哥本哈根大学获得数学博士学位，导师为 Ian Kiming 和 Fabien Pazuki。此后，他先后在法国里昂高等师范做爱视频、德国波恩马克斯·普朗克数学研究所和德国汉诺威莱布尼茨大学从事博士后研究，合作导师分别为 Fran?ois Brunault、Pieter Moree 和 Ziyang Gao。2024 年起，在意大利Messina大学担任终身轨研究员（RTT）。
