Korman Center, Room 245, 15 S. 33rd Street, Philadelphia, PA 19104
Colloquium: Free Convex Analysis and Semialgebraic Geometry
Wednesday, January 15, 2014
3:00 PM-4:00 PM
Scott McCullough, Department of Mathematics, University of Florida
The talk will survey aspects of the theory of free - freely non-commutative - convexity and semi-algebraic geometry. In this context free (matrix) convex sets, which appear in the theory of operator systems and spaces, have a simple concrete matrix theoretic formulation. A free semialgebraic set is the solution set of a system of matrix or noncommutative polynomial inequalities. The pairs of symmetric matrices (X,Y) of the same size such that I-X^4-Y^4 is positive definite provides an elementary example. Free analogs of classical results on weighted sums of squares representations often have cleaner statements than their commutative counterparts, particularly in the presence of convexity. As for motivation, free convex semialgebraic sets arise naturally in certain engineering systems problems determined by a signal flow diagram.