Abstract:
Transfinite diameter is a geometric notion that plays a central role
in classical potential theory and complex analysis. It can also be
defined in terms of univariate polynomials. In several complex
variables and pluripotential theory, the Fekete-Leja transfinite
diameter is a natural generalization. An important study of it was
Zaharjuta's 1975 paper. His methods for studying transfinite diameter
combined algebra and analysis, i.e. manipulating polynomials, and
taking limits. The algebraic part in this case was relatively
trivial. I am interested in studying transfinite diameter on an
algebraic variety. Recently with David Cox (Amherst, MA), we were
able to adapt Zaharjuta's techniques to study transfinite diameter on
varieties that behave “nicely” at infinity. Almost all of the
additional work is in the algebra. I will describe our work and
illustrate it with concrete examples.
Language: English
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