Invited Talks

: If we graph the simplest quadratic, we see that its range, or its image, consists of all positive numbers and zero. Let us extend this idea by instead evaluating polynomials on square matrices whose entries come from the complex numbers. A version of the L'vov-Kaplansky conjecture states that the image of a multilinear polynomial evaluated over matrices, with entries from the complex numbers, is a vector space, which is an algebraic structure that much is known about. We will consider this problem in a slightly different context by adding in some elements to the complex numbers that are not necessarily commutative. We will see how the existence of such elements changes the structure of our polynomials and their images. The talk will be accessible to anyone interested in mathematics.