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Algebraic groups and Lie algebras


School of Mathematics

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About the Project

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.

Funding Notes

This research project is one of a number of projects in the School of Mathematics. It is in competition for funding with other PhD projects. Usually the projects which receive the best applicant will be awarded supported.

Normally scholarships are only available to UK or EU citizens. Other nationals who are normally resident in the UK or those who have been resident in the UK for a period of 3 years or more are also eligible.

For information on deadlines see
https://www.birmingham.ac.uk/schools/mathematics/phd/how-to-apply.aspx

Students with the correct qualifications and access to independent funding are also welcome to apply.
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