Probabilistic Operator Algebra Seminar: The Waring and Other Problems for Noncommutative Polynomials

Seminar | April 16 | 12:30-2 p.m. | 748 Evans Hall

 Bill Helton, UC San Diego

 Department of Mathematics

A homogeneous noncommutative degree $d$ polynomial $p$ has a $t$-term real Waring (resp. complex Waring) decomposition provided that $p(x)$ can be written as the sum of $t$ terms of the $d^{th}$-power of linear functions of $x$, i.e. \[ p(x)=\sum _{s=1}^t [ A^s_1x_1 + A^s_2x_2 + ... A^s_gx_g]^d \] with real (resp. complex) numbers $A_j^s$. The talk will analyze this, some consequences and extensions.

If time permits there will be a sketch of some other recent results drawn from free analysis.