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Explore recent applications of model theory to algebraic dynamics in this mathematical colloquium lecture. Learn how model theory, a branch of mathematical logic with established applications to algebra, geometry, and number theory, has been extended to address problems in algebraic dynamics. Discover the historical context of model-theoretic applications to algebraic dynamics, including foundational work by Chatzidakis-Hrushovski and Medvedev-Scanlon from the 1990s. Examine cutting-edge research developments arising from collaborative work with Moshe Kamensky, Jason Bell, and Matthew Satriano, which draws inspiration from the analogy between algebraic dynamics and algebraic differential equations. Understand how these recent advances contribute to the birational classification problem for algebraic dynamical systems, representing a significant frontier in the intersection of mathematical logic and dynamical systems theory.
