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Graduate Student Analysis Seminar

Polynomial Convexity

Chloe Wawrzyniak, Rutgers University

Location:  Hill GSL
Date & time: Monday, 04 December 2017 at 5:00PM - 6:00PM

  A compact set X in C^n is polynomially convex if for every x outside X, there is a polynomial P such that |P(x)| is strictly larger than the supremum of |P| over X. A natural question is to classify which sets are polynomially convex. In one complex dimension, the answer is well-known. But in dimension 2 and higher, this question is still an area of active research. Many of the proofs in this area are long, technical, and require extra background. So, we will spend most of our time playing with examples while assuming some major results. If there is time and interest, I can also discuss some applications of polynomial convexity and why this question is important.