[Turkmath:3252] Sabancı University Mathematics Colloquium - Tuesday at 12:40 in FENS L035

[Michel Lavrauw]

You are cordially invited to the Mathematics Colloquium at 12:40 in the FENS building on Sabancı Campus in room L035 on Tuesday 2 October 2018.

Sione Ma'u (University of Auckland, New Zealand)
Title: Polynomial degree via pluripotential theory

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.

Kind regards,
Michel Lavrauw.
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