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Explore how quantum and classical mechanical processes can be represented through affine Lagrangian relations between finite-dimensional vector spaces in this mathematical colloquium talk. Learn about the semantic foundations of mechanical processes and discover the accompanying ZX-calculus-style graphical language that provides syntactic representation. Examine extensions of both syntax and semantics to more expressive mathematical settings, including Gaussian probabilistic behavior and discrete-time evolution systems. Gain insights into the mathematical frameworks that bridge categorical approaches to physics with practical computational representations, presented through rigorous mathematical exposition suitable for researchers in category theory, quantum computing, and mathematical physics.
