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Session

RAG3: Real Algebraic Geometry Location: M629 Session Chair: Daniel Plaumann Session Chair: Claus Scheiderer

Presentation 1

Semialgebraic algorithms for cutting polytopal measures Marie-Charlotte Brandenburg1, Jesús A. De Loera2, Chiara Meroni3 1: Ruhr-Universität Bochum; 2: University of California, Davis; 3: ETH Institute for Theoretical Studies In a joint work with Marie-Charlotte Brandenburg and Jesús A. De Loera, we develop exact polynomial time algorithms for ham-sandwich and centerpoint problems for rational polytopal measures. Our approach encodes cuts of prescribed proportions via a piecewise rational cap-volume function, reducing the problem to semialgebraic feasibility. This yields algorithms to decide existence, describe, count, and sample cuts. We also show that spaces of deep affine flats are semialgebraic, recovering the centerpoint set of a convex body as a floating body.