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Santaló Geometry of Convex Polytopes

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EMGW02 - Applied and computational algebraic geometry

The Santaló point of a convex polytope is the interior point which leads to a polar dual of minimal volume. This dual volume replaces other natural objective functions in convex optimization, such as the logarithmic barrier minimized by the analytic center. When translating the facet hyperplanes, the Santaló point traces out a patchwork of semialgebraic sets. I will describe and compute this geometry using algebraic and numerical techniques. I will also explore connections with statistics, optimization and physics. This is joint work with Dmitrii Pavlov.

This talk is part of the Isaac Newton Institute Seminar Series series.

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