Student: 
Eric Wayman 
School: 

Email: 

Research Area(s): 
Symplectic Geometry 
Project Name: 
Polytopes related to Symplectic Geometry and Homotopy Theory 
Faculty Advisor: 
Dr. Cristopher Woodward, Professor of Mathematics 
Research Partner: 
Project DescriptionWe're attempting to classify which of the multiplihedra and "plethorahedra" are convex polytopes. A convex polytope is the convex hull of a finite set of points in n dimensional space. The simplest multiplihedra is the associahedron. The dth associahedron Kd is a complex of dimension d2 whose vertices correspond to the possible ways of pracketing d variables. An edge is formed between two vertices when the two bracketed expressions vary at a single set of parentheses. Stasheff showed each associahedra has a realization as a polytope. Which multiplehdra and plethorahedra have realizations as polytopes is an open question. 