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Algebraic Dynamics and the Model Theory of Difference Fields

Introductory Workshop: Model Theory, Arithmetic Geometry and Number Theory February 03, 2014 - February 07, 2014

February 07, 2014 (02:30PM PST - 03:30PM PST)
Speaker(s): Alice Medvedev (City College, CUNY)
Location: MSRI: Simons Auditorium
Video

Abstract

An algebraic dynamical system is a variety $X$ with a self-morphism $F : X \rightarrow X$. Difference equations are a natural tool for understanding such discrete dynamical systems, just as differential equations are natural toop for understanding continuous dymanical systems.  "Model theory of difference fields" (1999) by Chatzidakis and Hrushovski is a beautiful application of geometric stability theory (one of the shiniest parts of modern model theory!) to algebraic difference equations. Several results in arithmetic dynamics have now been obtained through this model-theoretic way of thinking about difference equations. I will describe several of these, including the work on Chatzidakis and Hrushovski on descent in algebraic dynamics and my work with Scanlon on coordinate-wise polynomial dynamics.

Supplements
20090?type=thumb Medvedev notes 2.16 MB application/pdf Download
Video/Audio Files

v1262

H.264 Video v1262.mp4 336 MB video/mp4 rtsp://videos.msri.org/data/000/019/901/original/v1262.mp4 Download
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