Graph Varieties

Meeting Time: Apr. 5, 2010, 2:35pm, Avery 351

Abstract: A graph variety is a space that parametrizes arrangements of points and lines that "look like" a given graph: that is, subject to containment relations given by the vertex-edge incidences of the graph. Many fundamental algebraic and geometric properties of graph varieties including defining equations, component structure, and homology groups, can be described explicitly in terms of the graph; the relevant combinatorial tools include rigidity theory and the Tutte polynomial. I'll review some of my earlier work on graph varieties and talk about my current work (joint with Tom Enkosky) about generalization to higher-dimensional ambient spaces. I'll try to make the talk self-contained and accessible to graduate students.