Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks

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Characters of symmetric groups: sharp bounds and applications (2008, background): “where Irr(G) is the set of complex irreducible characters of G. The zeta function of Sn plays a major role in this paper (see [ LiSh2 ] for some of its properties).”
Finite covers of random 3-manifolds (2005, background): “Everitt manages to build explicit covers which realize these groups. Recently, Liebeck and Shalev have given another proof which studies the question from a very different probabilistic point of view [LS1]. Theorem 7.1 suggests that we might expect the answer to Question 7.6 to be yes because |H2(An”
Counting arithmetic lattices and surfaces (2008, methodology): “The proof is a modication of the one given in [ LiSh ], it relies heavily on bounds for the character values of symmetric groups.”
Fuchsian groups, finite simple groups and representation varieties (2005, methodology): “applications: for instance, when G is a symmetric group, this was studied in [36, 41, 32 ], with applications to random walks, subgroup growth and coverings of Riemann surfaces.”
Word maps and Waring type problems (2007, unknown): “We need the following two results from [LiSh2], related to character degrees.”
Commutator maps, measure preservation, and T-systems (2007, methodology): “We conclude that in A n we have By Theorem 1.1 in [LiSh3], This completes the case G = A n and the constructive proof of Theorem 1.5.”