Title: An Introduction to Cone Ranks of Polytopes

Abstract: An extended formulation of a polytope P is a set Q coupled with an 
affine map L such that P=L(Q). For some polytopes, such as the permutahedron, 
we can find an extended formulation where Q is much simpler than P. Recently, 
much work has been done seeking to answer when and how such formulations can be 
found. In this talk, I will begin by presenting the connection between linear 
extended formulations and nonnegative rank as introduced by Yannakakis (1991). 
Then, I will discuss how this idea extends to the more general setting of cone 
rank as introduced by Gouveia, Parrilo, and Thomas (2011). Recent results 
concerning the PSD rank of polytopes will also be discussed. No material beyond 
Math 514 will be assumed for this talk.