Speaker: Virgile Tapiero (Institute for Mathematics and Fundamental Physics)
Time: 14:30-15:30, Jul 18, 25, 2025
Venue: room 1329, Building 1 (Section A), New Campus, Shanghai Institute for Advanced Studies, USTC & Tencent Meeting ID: 942 663 0176, password: 202501
Talk 1:
In this presentation, I will give an introduction to complex dynamics. I will start with some historical reminders in dimension 1, presenting a few tools that lie at the heart of modern techniques, such as potential theory and ergodic theory. Then, I will explain the questions that interest researchers in modern dynamics, in dimension 1 or higher, and if time permits, I will try to make a connection with famous problems that do not directly involve dynamics but for which recent progress has been made using complex dynamics methods.
Talk 2:
This presentation will be a continuation of the one initiated last week. This time, I will focus on the case of higher dimension. We will see that the concepts introduced last week in the one-dimensional setting can be extended to higher dimensions. The main difference between dimension one and higher dimensions is essentially the emergence of a new concept: the notion of positive currents. This concept generalizes the notion of functions or measures, which are predominant in dimension one. Currents are formally differential forms, but with non-smooth coefficients, they serve as a bridge between geometry and analysis, and are particularly well-suited for addressing problems in dynamics. I will also present some new results I have recently obtained on the dynamics of endomorphisms of projective spaces.
For more information, please visit: https://vtmaths.github.io/imfp-igp-seminar/index.html
