John McCarthy, Washington University in St. Louis
“An introduction to noncommutative functions”
A holomorphic function can be thought of as a generalized polynomial. A non-commutative holo- morphic function is a generalization of a polynomial in non-commuting variables. Why would anyone look at them? Because physicists, engineers (and weird mathematicians called operator theorists) like to look at functions of matrices, and the matrices may not commute.
We will explain the ideas behind non-commutative functions, originating with the work of J.L. Taylor in the early 70’s. As a consequence, we will show that a generic solution (X,Y) of the matrix equation X2 + 2XY + 3Y2 + 4X3 + 5XY2 + 6Y4 = 7I must actually commute (so the study of non-commutativity can shed light on commutativity).
MC 5501
Refreshments will be served in MC 5403 at 3:30 p.m. Everyone is welcome to attend.