**abstract:**
Transfinite diameter is a geometric notion that plays a central role in classical potential theory and complex analysis. 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 transfinite diameter on an algebraic variety. Recently with David Cox (Amherst, MA), we adapted Zaharjuta's techniques to study transfinite diameter on algebraic varieties in $\mathbb{C}^{n$} that behave ``nicely'' at infinity. Almost all the additional work is in the algebra. I will describe our work and illustrate it with concrete examples.

Sat 28 Mar, 9:50 - 10:30, Aula Dini

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