|Location:||MSRI: Simons Auditorium|
Filling invariants measure the difficulty of filling a closed curve or sphere in a space with a ball. This is particularly easy in nonpositively curved spaces, but it is more complicated in subsets of nonpositively curved spaces, such as lattices in symmetric spaces. Gromov and Thurston conjectured that the difficulty of filling a sphere in such a lattice depends on the dimension of the sphere and the rank of the symmetric space. This conjecture has been proven in several special cases, and in this talk, I will describe the geometry behind the conjecture and sketch a proof of the general case. This is
joint work with Enrico Leuzinger.