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 ...

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 ...

Complex geometry and algebraic geometry are intertwined disciplines that investigate spaces defined by complex analytic structures and polynomial equations. Complex geometry focuses on complex ...

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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 ...

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 ...

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.