Physics Paradigm Challenge

Instead of tracking every single particle, physicists figured out they can just measure the volume of a giant, invisible 'jewel' to explain how the universe works.

March 27, 2026

Original Paper

Landau Analysis in the Grassmannian

Benjamin Hollering, Elia Mazzucchelli, Matteo Parisi, Bernd Sturmfels

arXiv · 2603.25454

The Takeaway

Rather than using messy equations to describe colliding particles, physicists have found that the results match the shape of a geometric object called an "Amplituhedron." This research explores the mathematical rules of this object, suggesting that our reality might be a projection of a higher-dimensional geometric shape.

From the abstract

Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discriminants and resultants are identified with Hurwitz and Chow forms of incidence varieties in products of Grassmannians. We study their degrees and factorizations, and the kinematic regimes in which the fibers of the Landau map are rational or real. Identifying this map with the amplituhedron map on positroid varieties, and