## Welcome!

Welcome to the Diffeomorphism and Geometry Group web page. The "Diagonal Sand" image represents the two concepts of*diffeomorphisms*and

*geometry*that are used in physics to mathematically describe the forces in nature.

The rolling hills of sand on the left represent the
concept of curvature which is known as *geometry*.
Geometry is used in mathematical theories called gauge
theories that are used to describe the strong nuclear force,
the weak nuclear force, and electromagnetism. Geometry
is also used in Einstein's theory of General Relativity which
is the present day accepted mathematical theory of
gravitation.

On the other hand, the smooth sand on the right corresponds
to the smooth coordinate transformations that are called *diffeomorphisms*

in
mathematics. Diffeomorphisms mathematically encode a
powerful physics principle that states that
physical events should not be tied to a particular point of
view. Diffeomorphisms provide the maps from
one point of view to another so these different view points
can agree on what has happened in a physical event.

Beneath it all are the tiny grains of sand. These tiny ingredients correspond to the quantum make up of the forces of Nature. A consistent mathematical description of these forces which includes their quantum nature is an active part of the research in theoretical physics.