讲座内容：

Determining an upper bound on s for vertex-primitive s-arc-transitive digraphs has been an open problem of considerable interest since a question asked by Praeger in 1990. Although much progress has been made and an upper bound is conjectured to be 2, a complete classification for s=2 remains out of reach. In this paper, we prove that the tight upper bound on s for finite vertex-primitive s-arc-transitive Cayley digraphs is exactly 2. Furthermore, we completely characterize the structure of these digraphs when s=2.