Fourier and small ball estimates for word maps on unitary groups

Nir Avni, Itay Glazer, Michael Larsen

To a non-trivial word $w(x_1,...,x_r)$ in a free group $F_r$ on $r$ elements and a group $G$, one can associate the word map $w_G:G^r\to G$ that takes an $r$-tupl…