Positive Geometries and Wonderful Compactifications

  • Raluca Vlad (Brown University)
G3 10 (Lecture hall)


A positive geometry consists of a real projective variety and a semialgebraic subset (its “positive part”), together with a canonical rational form which satisfies a recursive definition when restricted to the boundary of the semialgebraic set. Positive geometries have been objects of interest in physics, and have recently started being explored mathematically. In my talk, I will focus on hyperplane arrangements in projective space. Regions in a hyperplane arrangement complement are polytopes, which are known to be positive geometries. I will discuss when such a region remains a positive geometry after taking the wonderful compactification of the arrangement. This talk is based on work in progress with S. Brauner, C. Eur, and L. Pratt.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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