A quantum ergodic theorem for mapping class groups action on character   variety
  We state a theorem relating the ergodicity of the action of a given subgroup of the mapping class group of a surface on the character variety, to the asymptotic of its invariant subspaces through the Witten-Reshetikhin-Turaev representations. As application we give an asymptotic result on the spin decomposition arising in TQFT. 
Julien Korinman
math-ph math.AT math.MP