## Mathematics Colloquium: Polynomial degree via pluripotential theory

### Mathematics Colloquium: Polynomial degree via pluripotential theory

Speaker: Sione Ma

Title: Impact of Renewables on System Protection

Date/Time: October 2, 12:30

Place: FENS L035

Abstract: Given a complex polynomial $p$ in one variable, $\log|p|$ is a subharmonic function that grows like $(deg p)\log|z|$ as $|z|\to\infty$.  Such functions are studied using complex potential theory, based on the Laplace operator in the complex plane.

Multivariable polynomials can also be studied using potential theory (more precisely, a non-linear version called pluripotential theory, which is based on the complex Monge-Ampere operator).  In this talk I will motivate and define a notion of degree of a polynomial on an affine variety using pluripotential theory (Lelong degree).  Using this notion, a straightforward calculation yields a version of Bezout's theorem.  I will present some examples and describe how to compute Lelong degree explicitly on an algebraic curve.  This is joint work with Jesse Hart.

Contact: Michel Lavrauw