Using category theory to organize and operate on information

David Spivak
Department of Mathematics, Massachusetts Institute of Technology

Category theory has become a fundamental part of pure mathematics because of its ability to bridge different disciplines and to provide broadly-applicable conceptual structures and tools, helping mathematicians to operate more effectively on diverse collections of objects. However, it has more recently branched out, making major contributions in fields like physics and computer science. It's power being to organize and make connections, I believe category theory also has much to offer in the fledgling field of data science, where information from diverse sources needs to be integrated and made useful. Finding useful structures that span diverse disciplines is the overarching theme of the talk.
First I will discuss a broad framework from category theory, namely that of operads, which formalizes a very general notion of composition. I will give several small examples from materials science, the pharmaceutical industry, and computer science. Then I will explain in some detail another application: a new approach to solving systems of nonlinear systems of equations or inequalities. Finally, I will show how precisely the same compositional framework also gives tools for combining data from multiple sources, as well as for analyzing interconnected dynamical systems.
Attendees will not need any category theory background to understand the talk.