New light on classical problems in representation theory 

Dr Hankyung Ko will receive funding from the Knut and Alice
Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematics, Uppsala University.

The planned project aims to investigate certain algebraic structures within representation theory. Such a structure could consist of all symmetries of an object – such as reflections and rotations – that are collected in an algebraic unit called a symmetry group. 

As early as the years around 1900, the pioneers of representation theory, Issai Schur and Emmy Noether, realised that many mathematical objects can be studied very effectively via their symmetry groups. This approach has not only had a profound influence on the development of modern mathematics but also played a decisive role in the emergence of the standard model of particle physics, and proved fruitful in other areas, such as theoretical physics, chemistry, computer science and programming.

In modern representation theory, fundamental questions are often scrutinised by studying categories, which are abstract mathematical structures that consist of objects and the relationships between them. Categories are powerful tools, both for formulating and proving general propositions and for performing explicit calculations. The main objective of the project is to deepen the understanding of Hecke categories and to clarify their role in representation theory.

The calculations performed within the project are well suited to various types of computer support and utilise recent advances in computational methods. Some results are expected to have direct implications in representation theory, while for others, their application to representation theory constitutes an important part of the project.

Photo: Mikael Wallerstedt