Undergraduate Seminar: "Combinatorics and geometry: a tour of the Grassmannian and some of its decompositions."

Speaker: Ryan Roach, Washington University in Saint Louis

Abstract: In this expository talk we introduce the Grassmannian, the space of k-dimensional subspaces of an n-dimensional vector space, and some of its more combinatorially-flavored properties. We begin with the Plücker embedding, continue to Schubert cells and the Bruhat decomposition, and finish with the positroid cell decomposition. Along the way, we'll discuss some combinatorial objects, partitions, decorated permutations, and matroids, and, time permitting, might take a few detours into the land of motivation.

Host: Adeli Hutton