Analysis Seminar: "Partially convex noncommutative sets"

Abstract: Noncommutative convexity is ubiquitous in the sciences and engineering. In most applications of interest, however, the situation is not truly convex; one must allow for certain partial notions of convexity. We propose a general framework for partial noncommutative convexity, in both the matrix and operator settings, that contains the classically well-studied examples, such as biconvexity, as special cases. Main results include general partially convex analogues of the Effros-Winkler separation theorem for ordinary matrix convex sets.  Applications are discussed in the directions of partially convex free semi-algebraic sets. This talk is based on joint work with M. Jury, I. Klep, S. McCullough, and J.E. Pascoe.

Host: Brett Wick