Joint IAS/PU Groups and Dynamics Seminar

Let w be a word in a free group. A few years ago, Magee and I, relying on a work of Calegari, discovered that the stable commutator length of w, which is a well-studied topological invariant, can also be defined in terms of certain Fourier coefficients of w-random unitary matrices. 

But there are very natural ways to tweak the random-matrix side of this story: one may consider, for example, w-random permutations or w-random orthogonal matrices, and apply the same definition to obtain other "stable" invariants of w. Are these invariants interesting? Do they have, too, alternative topological/combinatorial definitions?

In a joint work with Yotam Shomroni, we present concrete conjectures and begin to answer some of them.

No background is assumed - I will define all notions