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