Analysis and Probability seminar

Let $A$ be an algebra and let $f=f(X_1,\dots,X_m)$ be a noncommutative polynomial.  Set $f(A)=\{f(a_1,\dots,a_m)\,|\,a_1,\dots,a_m\in A\}$. The Waring problem for $A$ is to find a positive integer $N$ such that, for any $f$, every element in span$f(A)$ can be written as a linear combination of  $N$ elements from $f(A)$. We will discuss it for different matrix algebras.