in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.

The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular, it is shown that for a given quadratic operator, the rank-k numerical range, the essential numerical range, and the q-numerical range are elliptical disks; the c-numerical range is a sum of elliptical disks, and the Davis-Wieland...

A bstract We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described $$ \mathfrak{sl}(2)/\mathfrak{u}(1) sl 2 / u <m...

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.

These are lecture notes of a course given by Alex Kumjian at the RMMC Summer School at the University of Wyoming, Laramie, June 1-5, 2015. Warning: little proofreading has been done.