Doron Puder, Tel Aviv University and the IAS
Event Date
2025-02-04
Event Time
03:30 pm ~ 04:30 pm
Event Location
Penn (David Rittenhouse Lab 4C8)
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.