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Discrete Math Seminar
March 5, 2013 @ 3:00 pm - 4:00 pm
Speaker: Cynthia Vinzant (University of Michigan)
Title: The central curve of a linear program
Abstract: The central curve of a linear program is an algebraic curve specified by a hyperplane arrangement and a cost vector. This curve is the union of the various central paths for minimizing or maximizing the cost function over any region in this hyperplane arrangement. I will discuss the algebraic properties of this curve and its beautiful global geometry, both of which are controlled by the corresponding matroid of the hyperplane arrangement.