Posted on 24 May 2017
Dr Geranios, Associate Lecturer in Mathematics, won the fellowship for his proposal 'Problems in Modular Representation Theory of General Linear Groups'. Dr Geranios is an expert in the representation theory of algebraic groups. Over the years he has solved longstanding problems and answered important questions in this fascinating research area of mathematics.
One of the main themes in life and science is symmetry. The study of symmetry has been prevalent across various scientific disciplines and it is one of the most important concepts in the way we describe the universe. Representation theory is the most effective way of studying symmetry and connects pure mathematics with applied sciences. The main idea is that one investigates the interactions of the algebraic object that we call a group with different structures, these are the representations, and in this way has a powerful method to obtain vital information for these structures, but also for the group itself.
Every representation can be composed of smaller pieces, the so-called irreducible representations, which are the elementary particles of this theory. Therefore in order to understand the big picture it becomes essential to describe the irreducible representations and the ways that they build a representation. These two problems have been the centre of attention of the mathematical community for many decades. Surprisingly enough these days we know even less around this subject than what we knew some years ago.
In recent years Dr Geranios together with his main collaborator, Professor S. Donkin (York), have developed radical methods and approaches to attack these problems. Based on these novel ideas, Dr Geranios aims with this fellowship to tackle these fundamental problems in mathematics and shed light on the mysterious nature of the irreducible representations and their behaviour.
These fellowships are awarded to outstanding scientists in the UK who are in the early stages of their research career and have the potential to become leaders in their field.
Further information about the Royal Society University Research Fellowships can be found at https://royalsociety.org/grants-schemes-awards/grants/university-research/