SEMF | [Bad Audio] David Spivak | Applied Category Theory: Toward a Hard Science of Interdisciplinarity @SEMF | Uploaded December 2023 | Updated October 2024, 3 hours ago.
Talk kindly contributed by David Spivak in SEMF's 2023 Interdisciplinary Summer School (semf.org.es/school2023)

Full session: youtube.com/watch?v=_sVFZv9tYdA

TALK ABSTRACT
Effective interoperation between multiple scientific disciplines is crucial to systems engineering. Can the study of interoperability---the working negotiations and hand-offs between theories and models---itself be made into a hard science? Hard sciences are based on mathematics, so this would require a mathematics of interoperability, a mathematics whose subject consists of the bridges and analogies that make data- and model-integration actually work. I propose that category theory serves this purpose exceptionally well.

In this talk, I will give evidence for the above claim, and without assuming the audience has seen any category theory before. I will focus on operads, which offer a framework for various forms of compositionality. In particular, I will discuss how operads model the interconnection of dynamical systems, provide a new method for solving systems of nonlinear equations, and explain how these two issues are connected category-theoretically. Finally, I'll explain how all this fits into a larger mathematical approach to interdisciplinarity.

DAVID SPIVAK
Personal Site: dspivak.net
Topos Institute Profile: https://topos.site/people/owen-lynch/

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