A talk about Babai’s PCC conjecture

Tomorrow morning (9am GMT) I am giving a seminar in Novosibirsk (virtually of course). The abstract is below. If you are interested in attending let me know I will give you the Zoom link.

Title: Nonschurian primitive association schemes with many automorphisms

Abstract: This talk is about primitive coherent configurations X of degree n with more than \exp(n^\epsilon) automorphisms, for constant \epsilon > 0. Babai conjectured that all such are so-called Cameron schemes, the orbital configurations of large primitive groups \mathrm{Sym}(m)^{(k)} \wr G for G \le \mathrm{Sym}(d). We will describe several families of examples that show Babai’s conjecture is actually wrong, strictly interpretted. In particular there is a primitive association scheme X of degree n = m^8 for any m \ge 3 such that \mathrm{Aut}(X) is imprimitive and |\mathrm{Aut}(X)| > \exp(m). But a slightly revised form of Babai’s conjecture is still plausible.