Tutte colloquium-Allen Knutson

Title:The mathematics of juggling

Abstract: I'll explain how to associate to any matrix a juggling pattern, with many examples demonstrated. This will give a decomposition of the Grassmannian Gr(k,n), of k-planes in n-space, into pieces indexed by juggling patterns. I'll explain how this "positroid decomposition" arises in (1) the very classical theory of "totally positive (real) matrices" (2) the characteristic p theory of "Frobenius splitting" and (3) Poisson geometry.