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Filling inequalities for lattices in symmetric spaces

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Robert Young (NYU)

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.