Explore advanced mathematical concepts in this Institute for Advanced Study lecture on the external activity complex of ordered matroid pairs and their relationship to Schubert varieties. Delve into how these constructions generalize the concept of external activity for matroid bases and single linear space Schubert varieties, particularly when one matroid is uniform of rank 1. Learn about the connection between Betti numbers of external activity complexes and Euler characteristics of tautological matroid classes, leading to a positive formula for Speyer's matroid invariant. Follow along as Andrew Berget presents ongoing research conducted with Alex Fink, offering insights into this sophisticated intersection of combinatorial and geometric mathematics.