How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

The field of algebraic geometry investigates the profound interplay between polynomial equations and geometric structures, providing a rich framework that unites abstract theory with practical ...

Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of polynomials.

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 ...

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 ...

Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams. Credit: Max Planck Institute for Mathematics in the Sciences How can the behavior of elementary particles ...

Mathematics and physics share a close, reciprocal relationship. Mathematics offers the language and tools to describe physical phenomena, while physics drives the development of new mathematical ideas ...