标题： 宇宙的代数与正几何：从粒子到星系 显示英文标题

标题： Algebraic and Positive Geometry of the Universe: from Particles to Galaxies

摘要： 近年来，代数、几何与组合数学与粒子物理和宇宙学的交叉领域取得了显著进展。 这一进步的核心在于粒子相互作用及其可观测量研究的双重表述：一方面，费曼的方法归结为复杂积分的研究；另一方面，则涉及到正几何的研究。 本文介绍了关键发展、数学工具以及推动代数几何、$D$-模理论、组合数学与物理学前沿发展的联系。 所有这些方面共同塑造了蓬勃发展的正几何领域，该领域旨在建立一种统一的数学语言来描述宇宙学和粒子物理学中的现象。 显示英文摘要

摘要： 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.