For a century, the Schrödinger equation has been the bedrock of quantum mechanics, successfully predicting how matter behaves as a wave. Yet, physics has lacked a fundamental explanation for why ...

The study of differential algebraic geometry and model theory occupies a pivotal position at the interface of algebra, geometry, and logic. Differential algebraic geometry investigates solution sets ...

The field of complex geometry, intertwined with Lie theory, represents a vibrant area where algebraic and differential techniques converge to unravel the structure of complex manifolds and their ...

Researchers have discovered a hidden quantum geometry inside materials that subtly steers electrons, echoing how gravity ...

Transactions of the American Mathematical Society, Vol. 365, No. 9 (SEPTEMBER 2013), pp. 4575-4632 (58 pages) In this paper, an intersection theory for generic differential polynomials is presented.

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 ...

The Fields Medal, the world’s highest honor for mathematical research, has gone to two mathematicians who forged new links between different branches of mathematics. The recipients–announced this week ...

One of the most striking outcomes of the surface-minimization framework is its ability to explain structural features that ...