Geometric group theory and discrete mathematics intersect in the study of groups through the lens of geometric and combinatorial structures. At its core, geometric group theory probes how algebraic ...

It is remarkable that despite the presence of large numbers of degrees of freedom, motion control problems are effectively solved in biological systems. While feedback, regulation, and tracking have ...

A new study published in Nature Physics introduces a theory of electron-phonon coupling that is affected by the quantum geometry of the electronic wavefunctions. The movement of electrons in a lattice ...

Jason Lotay explains how mathematicians studying special geometries are collaborating with physicists to explore M-theory, an 11-dimensional description of the world that unifies the various string ...

Arnold’s work was in an area of mathematics that concerns all the different configurations a physical system like bouncing billiard balls or orbiting planets can take. These configurations are encoded ...

The grandest project in mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the ...

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program. A group of nine mathematicians has proved the ...