[Amath-seminars] Thursday Seminar, Abbas Salemi Parizi, 4-5pm, Dempsey 104

Loyce M. Adams lma3 at uw.edu
Tue Feb 21 18:15:00 PST 2017


Hi All,

This Thursday, the department's visitor Professor Abbas Salemi
Parizi from Shahid Bohonar University of Kerman, Iran will be
speaking. His title and abstract are below. Please come to hear this
special speaker.

Thanks,
Loyce Adams

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TITLE:

A TASTE OF NUMERICAL RANGE: PROPERTIES, APPLICATIONS AND OPEN PROBLEMS

SPEAKER:

ABBAS SALEMI PARIZI
DEPARTMENT OF MATHEMATICS, SHAHID BAHONAR UNIVERSITY OF KERMAN, IRAN.

ABSTRACT:

The numerical range of A ∈ Mn(C) is denoted by W(A) as follows:
W(A) = {x∗Ax : x ∈ Cn,∥x∥ = 1}.
The subject has applications to many different branches of pure and
applied science and has a long and distinguished history. Two of the
most exciting developments are the study of rank-k numerical range,
Λk(A), and polynomial numerical hull of order k, V k(A), as follows:
Λk(A) = {λ ∈ C : PAP = λP,for some rank k orthogonal projection P},
V k(A) = {λ ∈ C : |p(z) ≤ ∥p(A)∥, for all polynomials p of degree k or less}.
These definitions are motivated by the study of quantum error cor-
recting codes and numerical solutions of linear systems. In this
lecture, new results on the numerical range, higher rank numerical
range and polynomial numerical hulls are studied. Moreover, some open
problems on these subjects are presented.



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