# 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.