Gabriel Pallier (University of Lille) – Filling loops in Lie groups

In a Riemannian manifold, the first filling function $F(l)$ measures the least area needed to fill all null-homotopic loops of length at most $l$ using minimal discs. In this talk I will focus on the first filling function for large loops in Riemannian Lie groups. This function is also known as the Dehn function and quantifies the complexity of the word problem from combinatorial group theory. I will review results of Cornulier and Tessera showing it is either exponential or polynomially bounded, and discuss some recent progress on the problem of estimating the degree of polynomial growth when it is polynomially bounded. This is joint work with Ido Grayevsky (Bristol).