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SUMMARY:Word Measures and Profinite Rigidity - Liam Hanany\, University of
  Cambridge
DTSTART:20251017T150000Z
DTEND:20251017T160000Z
UID:TALK234835@talks.cam.ac.uk
CONTACT:Will Cohen
DESCRIPTION:Given a word $w \\in F_{r}$ in a free group on $r$-generators\
 , and\na finite group $G$\, the word map $G&Hat\;{r} \\to G$ is the map ob
 tained\nby evaluating the word $w$ on the $r$-tuple of elements of $G$.\nT
 he word map yields a measure on the finite group $G$ by pushing\nforward t
 he uniform measure on $G&Hat\;{r}$. We will discuss these\nmeasures and th
 eir connection to conjectures regarding profinite rigidity\nof words in fr
 ee groups. We will then describe some techniques used\nto prove special ca
 ses of these conjectures by studying word measures\non symmetric groups. I
 f time permits\, we will also discuss how these\nideas are related to solu
 tions of equations in free groups and the\nnon-negative immersions of grap
 hs of free groups with cyclic edge\ngroups.
LOCATION:MR13
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