2025-08-20 マックス・プランク研究所
Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams (Collage)
© Max Planck Institute for Mathematics in the Sciences
＜関連情報＞
- https://www.mpg.de/25215172/the-shape-of-the-universe-revealed-through-algebraic-geometry
- https://www.ams.org/journals/notices/202508/noti3220/noti3220.html
宇宙の代数幾何学と正則幾何学：粒子から銀河まで
Algebraic and Positive Geometry of the Universe: From Particles to Galaxies
Claudia Fevola,Anna-Laura Sattelberger
Notices of the American Mathematical Society Published:2025
DOI:https://doi.org/10.1090/noti3220
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofold formulation of the study of particle interactions and observables in the universe: on the one hand, Feynman’s approach reduces to the study of intricate integrals; on the other hand, one encounters the study of positive geometries. This article introduces key developments, mathematical tools, and the connections that drive progress at the frontier between algebraic geometry, the theory of D-modules, combinatorics, and physics. All these threads contribute to shaping the flourishing field of positive geometry, which aims to establish a unifying mathematical language for describing phenomena in cosmology and particle physics.
