|Location:||MSRI: Simons Auditorium|
A Mustafin variety is a degeneration of projective space induced by a point configuration in a Bruhat-Tits building. The special fiber is reduced and Cohen-Macaulay, and its components form beautiful combinatorial patterns. For configurations in one apartment, these patterns are mixed subdivisions of simplices, and there is a tight connection to tropical convexity. In general, the components of the special fiber are rational varieties, and any blow-up of projective space along a linear subspace arrangement can arise.
We present a study of the two-dimensional building for PGL(3), joint with Dustin Cartwright, Mathias Haebich and Annette Werner, that classifies Mustafin triangles into 38 combinatorial types.