For every finite quasisimple group of Lie type G, every irreducible character χ of G, and every
element g of G, we give an exponential upper bound for the character ratio |χ(g)|/χ(1) with …

The classical Waring problem deals with expressing every natural number as a sum of g (k)
k-th powers. Recently there has been considerable interest in similar questions for non …

Character levels and character bounds for finite classical groups | Inventiones mathematicae
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We establish new characterizations of primitive elements and free factors in free groups,
which are based on the distributions they induce on finite groups. For every finite group $ G …

In this survey paper we show how character methods can be used to solve a wide range of
seemingly unrelated problems. These include commutators, powers of conjugacy classes …

We prove several results on products of conjugacy classes in finite simple groups. The first
result is that for any finite nonabelian simple groups, there exists a triple of conjugate …

In this paper we consider which families of finite simple groups $ G $ have the property that
for each $\epsilon> 0$ there exists $ N> 0$ such that, if $| G|\ge N $ and $ S, T $ are normal …

Let F k be the free group on k generators. A word w∈ F k is called primitive if it belongs to
some basis of F k. We investigate two criteria for primitivity, and consider more generally …

For a function $ f $ on the hypercube $\{0, 1\}^ n $ with Fourier expansion $ f=\sum_
{S\subseteq [n]}\hat f (S)\chi_S $, the hypercontractive inequality for the noise operator …

If G is a group, we say a subset S of G is product-free if the equation xy= z has no solutions
with x, y, z∈ S. In 1985, Babai and Sós [] asked, for a finite group G, how large a subset S⊆ …