6 papers · 1 filter
Positive Geometries from Cubic Surfaces
Bernd Sturmfels, Simon Telen
We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (…
The Algebraic Boundary of Graph Elliptopes
Monique Laurent, Francesco Maria Mascarin, Simon Telen
This paper studies the algebraic boundary of the elliptope of a graph . In particular, we completely characterize the algebraic boundary of whe…
Principal Matroid Determinants
Saiei-Jaeyeong Matsubara-Heo, Simon Telen
We develop a theory of principal determinants and hypergeometric systems for realizable matroids. Our framework parallels the toric theory of Gel'fand, Kapranov, and Zelevinsky (GK…
Toric Amplitudes and Universal Adjoints
Simon Telen
A toric amplitude is a rational function associated to a simplicial polyhedral fan. The definition is inspired by scattering amplitudes in particle physics. We prove algebraic prop…
Positive Geometry of Polytopes and Polypols
Simon Telen
These are lecture notes supporting a minicourse taught at the Summer School in Total Positivity and Quantum Field Theory at CMSA Harvard in June 2025. We give an introduction to po…
What is Positive Geometry?
Kristian Ranestad, Bernd Sturmfels, Simon Telen
This article serves as an introduction to the special volume on Positive Geometry in the journal Le Matematiche. We attempt to answer the question in the title by describing the or…