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Student: |
Eric Wayman |
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School: |
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Email: |
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Research Area(s): |
Symplectic Geometry |
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Project Name: |
Polytopes related to Symplectic Geometry and Homotopy Theory |
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Faculty Advisor: |
Dr. Cristopher Woodward, Professor of Mathematics |
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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 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. |