In quantum mechanics, the geometry of quantum states has emerged as a powerful framework for understanding phenomena ranging ...

One of the first collaborations Xinyi Yuan and Wei Zhang ever undertook was a trip to the Social Security office. It was the fall of 2004 and the two of them were promising young graduate students in ...

A new theory aims to explain how the complex vertebrate body, with its skeleton, muscles, nervous and cardiovascular systems, arises from a single cell during development and how these systems evolved ...

LANL researchers (2026) validated Schrödinger's color perception theory using advanced geometry. Color perception is non-Riemannian, explaining diminishing returns in color differences. The model ...

When speaking of our universe, it's often said that "matter tells spacetime how to curve, and curved spacetime tells matter how to move." This is the essence of Albert Einstein's famous general theory ...

Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces ...

Algebraic geometry and number theory intersect in the study of solutions to polynomial equations and their symmetries. Algebraic geometry provides a language of schemes and varieties to capture ...

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...