05C50 Online Seminar: Roghayeh Maleki

An association scheme X on a finite set V is a highly-regular partition of the edge set of the complete graph on V. The Terwilliger algebra $T_v$ of X with respect to a vertex $v\in V$ is an algebra defined using the neighbours of v in each graph in the partition X. 

The algebra T_v satisfies the inclusions $T_0 \subseteq T_v \subseteq \widetilde{T}$, where T_0 is a certain subspace, and $\widetilde{T}$ is the centralizer algebra of the stabilizer of v in the automorphism group of X.

Roghayeh Maleki studies the association schemes arising from strongly-regular graphs whose Terwilliger algebras are as small as possible in the sense that $T_0 = T_v = \widetilde{T}$. A strongly-regular graph $\Gamma$ is called triply transitive if  (1) its automorphism group $\operatorname{Aut}(\Gamma)$ is transitive, and (2) its Terwilliger algebra coincides with both its subspace $ T_0$ and $\widetilde{T}$. In this talk, Maleki will present a complete classification of triply-transitive strongly-regular graphs.

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