Path signatures in convex geometry

Abstract: How can one compute the volume of the convex hull of a curve? I will try to answer this question, for special families of curves. This is a joint work with Carlos Améndola and Darrick Lee. We generalise the class of curves for which a certain integral formula works, using the technique of signatures. I will then give a geometric interpretation of this volume formula in terms of lengths and areas, and conclude with examples and an open conjecture.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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