Counting objects up to isomorphism

June Huh, IAS
Fine Hall 322

Given a sufficiently simple finite structure X, let’s count the number of nonisomorphic subobjects of X according to their sizes. 

It appears to me that the count obeys a universal principle that is independent of the object and what we mean by an isomorphism. I will demonstrate the heuristic principle with graphs, simplicial complexes, configurations, abelian groups, and representations. No background beyond linear algebra will be needed to enjoy the talk.