MIT Combinatorics Seminar


Satyan Devadoss  (Williams College)

Wednesday, November 17, 2004    4:15 pm    Room 2-338


The associahedron (or Stasheff polytope) is an object appearing in numerous areas of mathematics, from homotopy theory (operads), configuration spaces (particle collisions), statistics (phylogenetic trees), geometric group theory (Coxeter complexes), and combinatorics. Given any graph G, we construct a convex polytope based on G (dubbed the graph-associahedra) with some elegant properties. For example, when G is a path, we obtain the associahedron; when G is a cycle, we obtain the cyclohedron. These polytopes appear naturally with respect to simplicial Coxeter groups, and provide the tiling for certain compactified real moduli spaces.