Lie Theory

Lie theory is a branch of mathematics devoted to the study of symmetries that occur throughout mathematics and science.

For example the ancient classification of Platonic solids is seen nowadays as an instance of finding all ''finite symmetries`` in three-dimensional space. More recently the study of "continuous symmetries" of mathematical objects and structures known as Lie groups, introduced by Sophus Lie in the 1880's to study differential equations, has influenced many scientific disciplines.

One fundamental problem involves describing and classifying the structure and geometry of those symmetries and their various generalizations. Lie theory is also vital to number theory, differential equations, differential geometry, dynamical systems, and many other areas of mathematics and its applications.