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Intersection Bodies of Polytopes -
By computing the volume of slices of a polytope P, we can construct its intersection body IP, a fascinating (sometimes nonconvex) object coming from convex geometry. In joint work with Katalin Berlow, Marie-Charlotte Brandenburg, and Chiara Meroni, we study the intersection body of a convex polytope and prove it is a semialgebraic set. We further investigate its algebraic boundary and find an upper bound on the degree of its irreducible components. This talk will include at least a few nice pictures.
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