Pham Tiep

Word maps on finite simple groups

Given a nontrivial word w=w(x₁, ..., x_n) in the alphabet x₁, ..., x_n, consider the word map w: Gⁿ → G sending (g₁, ..., g_n) ∈ Gⁿ to w(g₁,  ..., g_n) and its image w(G)=w(Gⁿ), on any finite simple group G. How large is w(G)? In this talk we will discuss results, some well-known and some very recent, on this problem.