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Explore a groundbreaking approach to computational theory in this 30-minute conference talk that examines Topological Kleene Field Theories (TKFTs) as a novel framework for understanding computation. Discover how computations can be conceptualized as flows in bordisms, moving beyond traditional computational models to embrace smooth dynamical systems. Learn about the translation of abstract mathematical constructions into concrete computational terms, with explicit demonstrations of how dynamics can simulate different Turing machines. Gain insights into the intersection of topology, field theory, and computation theory, and understand how smooth dynamics provide a new lens for analyzing computational processes. Examine the practical implications of this theoretical framework and its potential applications in advancing our understanding of computation through geometric and topological perspectives.
