Fellows Seminar: Operad-like structures - from the "tree of life" and stemmata to algebra and geometry

Charles Darwin's first sketch of an evolutionary tree (1837)

By Vladimir Dotsenko, 2021 Fellow

An operad is a 50-year-old mathematical notion (the term is a portmanteau of the words "operation" and "monad") that formalises both the idea of self-similarity of sequences of objects and the idea of possible alternatives for changes of objects as time passes. I shall give a gentle overview of various situations where operads appear, and then talk about a generalization of the notion of an operad that I found in a recent research collaboration, which my coauthors (Adam Keilthy and Denis Lyskov) and I called a "reconnectad"; this notion appears quite naturally in studying toric varieties associated to graphs. A large part of the talk will be accessible to a curious non-mathematician.

• More information on Vladimir Dotsenko and his USIAS project: Homotopy invariants of wonderful compactifications