Britton Lecture Series: Model theory of difference fields

The second lecture by Thomas Scanlon, “Model Theory Of Difference Fields: The Logic Of Discrete Dynamical Systems, Algebraic Dynamics And Transcendental Number Theory”

Abstract:
The theory of difference fields gives a logical and algebraic account of discrete dynamical systems. Constructing a good model theoretic account of difference fields required building the general theory of simple theories. As with the theory of differential fields, this theory has been applied to problems in Diophantine geometry, the theory of algebraic dynamical systems, and to functional transcendence. With this lecture, I will focus on some newer results extending the logical theory to handle the kinds of difference equations appearing in practice, namely, when the solutions are sought as sequences, and then also to problems on functional transcendence for Mahler functions. (The new results are included in joint work with Alice Medvedev and Dang Khoa Nguyen.)

Dr. F. Ronald Britton was a former Professor of Mathematics at McMaster, and served as Chair of the Department of Mathematics. After his retirement, he endowed our annual Britton Lectures in memory of his late wife Helen E. Britton. The Britton Lectures have provided the University with a series of distinguished invited speakers since its beginning in 1978.

More info: https://www.math.mcmaster.ca/news-events/seminars-colloquia/britton-lectures.html