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Graduate Student Number Theory Learning Seminar

The pentagram map and arithmetic dynamics

Max Weinreich (Brown)

Location:  Zoom
Date & time: Tuesday, 23 March 2021 at 4:00PM - 5:00PM

Abstract: The pentagram map was introduced by Schwartz in 1992 as a dynamical system on polygons in the real projective plane. The map sends a polygon to the polygon formed by intersecting certain diagonals. This simple operation turns out to define an integrable system, a kind of dynamical system common in physics which resembles translation on a torus. We will talk about two ways to think about the pentagram map in terms of number theory. First, we'll look at the pentagram map in algebro-geometric terms to describe its behavior over finite fields. Then we'll describe how heights on number fields are used in practice to guess whether dynamical systems are integrable.

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