Sabancı University Algebra Seminars

Height growth rates in dynamical orbits
Wade Hindes
Sabancı Üniversitesi, Turkey
Özet : Let $V$ be a projective variety defined over a number field. A height function $h: V(\overline{\mathbb{Q}})\rightarrow\mathbb{R}$ is a tool for measuring the ``arithmetic complexity" of the points of $V$. In particular, one can often use height functions to detect geometric properties of the underlying variety. In this talk, we apply this philosophy to discrete dynamical systems. Namely, given a self map $f:V\rightarrow V$ and a point $P\in V$, then we are interested in the growth rate of $h(f^n(P))$ as we repeatedly iterate the map. What can this growth rate tell us about the variety $V$, the map $f$, and the point $P$? To investigate these questions, we survey basics properties of height functions, discuss several historically significant cases (e.g., elliptic curves and projective space), and motivate additional topics in the burgeoning field of arithmetic dynamics.
  Tarih : 30.10.2019
  Saat : 13:40
  Yer : in the FENS building on Sabancı Campus in room G035.
  Dil : English