Algebraic geometry has long provided a deep framework for understanding the solutions of polynomial equations through geometric lenses. In recent years, tropical geometry – a relatively young field – ...

Algebraic geometry, a venerable branch of mathematics, focuses on the study of algebraic varieties—geometric manifestations of polynomial equations—while cohomology provides a suite of invariants that ...

Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves. Like many people who would ...

Several fields of mathematics have developed in total isolation, using their own 'undecipherable' coded languages. Mathematicians now present 'big algebras,' a two-way mathematical 'dictionary' ...

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 ...

Alexander Grothendieck, one of the greatest mathematical minds of the twentieth century, died last Thursday (November 13). A recipient of the most prestigious honour in mathematics, the Fields medal, ...

In August, a team of mathematicians posted a paper claiming to solve a major problem in algebraic geometry — using entirely alien techniques. It instantly captivated the field, stoking excitement in ...

The term “moduli space” was coined by Riemann for the space $\mathfrak{M}_g$ parametrizing all one-dimensional complex manifolds of genus $g$. Variants of this ...

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.

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 ...