Slack Matrices for Polytopes and Polyhedra

Series: 
Student Algebraic Geometry Seminar
Friday, October 20, 2017 - 10:00
1 hour (actually 50 minutes)
Location: 
Skiles 114
,  
Georgia Institute of Technology
Organizer: 
We will introduce a class of nonnegative real matrices which are called slack matrices. Slack matrices provide the distance from equality of a vertex and a facet. We go over concepts of polytopes and polyhedrons briefly, and define slack matrices using those objects. Also, we will give several necessary and sufficient conditions for slack matrices of polyhedrons. We will also restrict our conditions for slack matrices for polytopes. Finally, we introduce the polyhedral verification problem, and some combinatorial characterizations of slack matrices.