D-companion
matrices and
geometry
of polynomials
Dr. Tuen Wai Ng
Abstract
In this
talk, we shall introduce a new type of companion matrices, D-companion
matrices. By using these D-companion matrices, we are able to apply
matrix theory directly to the study of geometry of polynomials. In fact, this
new approach will allow us to prove quite a number of old and new results in
geometry of polynomials. For example, we shall prove a one parameter family
version of Schoenberg-type inequality. We then apply the result to study the
relative locations of zeros and critical points of a polynomial and prove a
result related to Sendov conjecture for polynomials. The same method also
allows us to solve a higher order Schoenberg-type conjecture proposed by
M.G. de Bruin and A. Sharma. This is a joint work with W.S. Cheung.
Date: |
September 30, 2004 (Thursday) |
Time: |
4:00 – 5:00pm |
Place: |
Room 517, Meng Wah Complex |
|
All are welcome |
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