Special Groups and dynamics seminar (note the unusual time)

Speaker: Doron Puder (Tel-Aviv)


Title: Stable invariants and their role in word measures on groups


Abstract: Let w be a word in a free group. The stable commutator length of w is scl(w)=\inf cl(w^n)/n, where cl is the commutator length. Around 2009, Calegari discovered a "better" definition for scl, and used this definition to prove that scl(w) is computable and rational. Relying on Calegari's results, Magee and I later discovered that scl(w) can be equivalently defined using certain Fourier coefficients of w-random unitary matrices.
But scl does not show up in all Fourier coefficients of w-random unitary matrices. Is there an analogous result for arbitrary coefficients? Is there an analogous result for orthogonal groups or symmetric groups? I will present a new set of conjectures involving a plethora of new "stable invariants", some of which defined recently by Wilton, which we believe play the role of scl in these more general settings. In some cases we can prove the conjectures. 

All notions will be defined. This is joint work with Yotam Shomroni.