Title: Some open problems on distance-regular graphs 2: Subconstituents and connectivity

Abstract: If G is a primitive strongly regular graph, then for any vertex x, the subgraph of G induced by the vertices at distance 2 from x is always connected. In 2013, Brouwer asked for a generalization of this result to distance-regular graphs. We will discuss our results in this direction. This talk is based on joint work with Jack Koolen (USTC, China) and Paul Terwilliger (Univ of Wisconsin at Madison).