Title : Polynomials and plurisubharmonic functions
Speaker: Dr Sione Ma'u
Affiliation: University of Auckland
Time: 13:00 Wednesday, 27 June, 2018
Location: 303-257
Abstract
Complex polynomials are examples of entire holomorphic functions that satisfy certain growth restrictions, so we can study them using complex analysis. An example of this is an elementary complex analysis proof of the fundamental theorem of algebra. Polynomials are also related to potential theory: given a polynomial p (in one variable), log|p| is a subharmonic function, which can be thought of as a potential for the electrostatic field of point charges at the zeros of p.   Multivariable polynomials can be studied using holomorphic and plurisubharmonic (psh) functions (psh functions satisfy a non-linear version of potential theory based on the complex Monge-Ampere operator).   In this talk I will describe some complex analysis and potential theory in several variables and use it to derive a version of Bezout's theorem. This is joint work with Jesse Hart.

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