Seminar

Isoperimetric duality is a purely linear-algebraic statement about real and rational vector spaces; it is closely related to linear programming duality, although one does not seem to be directly provable from the other.  It generalizes old theorems in differential geometry (Cheeger's inequality) and geometric group theory (the Block--Weinberger characterization of amenability); there are a number of newer applications in quantitative algebraic topology (to be explained).  A weaker integral version makes use of the combinatorics of high-dimensional spanning trees.