Eric Wayman


Rutgers University


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:

Anna Fuller

Project Description

We'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 d-th associahedron Kd is a complex of dimension d-2 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.