Tutte Colloquium - Jorn van der Pol

Title: Large matroids: asymptotic enumeration

Abstract:

How many matroids are there on a ground set of a given size? Although the question is a very basic one, we only know the answer up to a constant factor in the exponent. A related question is that of asymptotic properties. What are the properties that we expect to see in a large random matroid? We are starting to understand which properties hold asymptotically, but the area is full of open problems. In this talk, I will review some of the bounds on the number of matroids as well as a number of results and conjectures about asymptotic properties.