This talk will introduce the concept of a functor from category theory assuming no prior acquaintance and highlight some applications of this notion. In the first part we will conceive of a functor as a bridge between two different mathematical theories. As a prototypical example we will consider the fundamental group construction from algebraic topology and explain how its functoriality leads to a proof of the Brouwer fixed point theorem. In the second part, we will explain how the search for a functorial clustering algorithm lead to a breakthrough in topological data analysis and speculate how a similar functors might be used to define combinatorial models of metric spaces.

Emily Riehl completed her PhD from the University of Chicago, and was a Benjamin Peirce and NSF Postdoctoral Fellow at Harvard. She holds an NSF CAREER grant and is the author of two highly-regarded books on Category Theory, as well as numerous publications in top journals.