# 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.