Geometric representation theory is a vibrant field that unites methods from algebraic geometry, category theory and homological algebra to probe the symmetries and invariants arising from algebraic ...

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 ...

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 ...

Geometric measure theory provides a rigorous framework for studying and quantifying the properties of sets and surfaces in Euclidean spaces. This discipline blends techniques from differential ...

A century after Erwin Schrödinger sketched out a bold vision for how we perceive color, scientists have finally filled in the missing pieces. A Los Alamos team used advanced geometry to show that hue, ...

One of the first collaborations Xinyi Yuan and Wei Zhang ever undertook was a trip to the Social Security office. It was the fall of 2004 and the two of them were promising young graduate students in ...

Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that ...

During the latter part of the 20th century, string theory was put forward as a unifying theory of physics foundations. String theory has not, however, fulfilled expectations. That is why we are of the ...

In this course we will consider the structure of (infinite) groups. For this, we will study actions of groups on interesting topological and metric spaces. The geometry of these spaces can be used to ...