Wednesday, October 14th, 2015
3:00pm - 4:00pm, in McCormack 2-205

David Spivak

MIT

Applied Category Theory

Abstract: Category theory (CT) is one of the most abstract branches of modern mathematics. However, it has become indispensible to modern research in pure mathematics because of its ability to make rigorous connections between objects of study within and across disciplines, from algebra to topology, from mathematical logic to probability theory to representation theory. More recently, category theory has begun to find applications outside of pure mathematics, e.g., in physics, computer science, linguistics, and materials science. The reason is roughly that CT is about articulating structures, as well as the relationships between structures, whether they be rings, spaces, or the schemes that organize databases. In this talk, I will present a very brief introduction to the field of applied category theory. I will explain a rigorous connection between two of the most successful applications of mathematical research, matrices and computer programs. This connection - called a functor - which maps the monoidal category of matrices to that of programs, preserves some but not all of the combinatorial structure of matrices. I will briefly mention other applications, such as discrete and continuous dynamical systems, that have a similar combinatorial structure to that of matrices. For this talk, I will assume no prior background in category theory, programming languages, or dynamical systems.