Modular Representation Theory of Finite Groups

As part of the representation theory of finite groups, to investigate properties of blocks of finite groups and their relationship to the defect group of the block.

In particular determination of the possible Morita equivalence classes of blocks and related invariants under suitable restrictions, as well as comparison of these invariants between blocks.

This is part of a current research theme in representation theory to investigate how invariants such as the defect group influence properties of the representations, and Morita equivalence is an important aspect of this.

The methods of investigation will be typical of pure mathematics, i.e., calculation and investigation of examples, identification of patterns arising, and construction of proofs. Some computer algebra will be involved.