Algebraic groups and Lie algebras

The University of Birmingham is well-known for its research into group theory, Lie theory and representation theory. The School of Mathematics has a vibrant and productive postgraduate environment that promotes research at the highest level.

Groups of continuous transformations, now known as Lie groups, have their origins in the work of Sophus Lie in the late 19th century, partly motivated by the wish to develop Galois theory for differential equations. Since then Lie groups and Lie algebras have been a central theme in mathematics. In the 1950s the ``analytic theory’’ was extended so that it also makes sense over arbitrary algebraically closed fields and spurned the area of mathematics now known as algebraic Lie theory. Nowadays algebraic Lie theory encompasses a variety of different areas, for example representation of algebraic groups and finite groups of Lie type, as well as Lie algebras and many related algebras. A common theme is the area is a strong interplay between algebra, geometry and combinatorics.

Dr Simon Goodwin is interested in supervising projects in a range of topics of Lie theory and representation theory. These include Lie algebras, W-algebras, algebraic groups and finite groups of Lie type.