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# Pi Mu Epsilon Undergraduate Talk – Thomas Mark, University of Virginia

## March 2 @ 5:00 pm - 6:00 pm

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Polynomial Convexity and a Nonlinear Triangle Inequality

Abstract: A subset of the plane is called convex if the line segment joining any two of its

points also lies in the set. The “convex hull” of a set is the smallest convex set

containing the given one. I’ll describe how convexity can be interpreted in terms of

linear polynomials, and how this leads to generalizations in terms of higher-degree

polynomials. Thinking about what it means for points to lie in the higher-degree

convex hull of a given set leads to an interesting geometric theorem about

triangles.

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