Algebraic geometry, the study of solutions to polynomial equations and their geometric properties, finds rich interplay with class field theory—a branch of number theory that classifies abelian ...

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major ...

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 the recent work by ...

Our research group is concerned with two lines of investigation: the construction and study of (new) cohomology theories for algebraic varieties and the study of various aspects of the Langlands ...

This is a preview. Log in through your library . Abstract Students see that geometric transformations—dilation and translation—correspond to algebraic parameters—m and b—in the familiar equation for a ...

One of the basic theorems in universal algebra is Birkhoff's variety theorem: the smallest equationally axiomatizable class containing a class K of algebras coincides with the class obtained by taking ...

The drive to get every student to take so-called college gateway courses has succeeded, a new federal study finds, but students taking Algebra 1 and Geometry classes are getting considerably less ...

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 ...