When an undergraduate at the University of Aberdeen I became particularly interested in algebra (especially modules) and mathematical logic (especially model theory) and I was able to combine these in my postgraduate research at the University of Leeds.
Indeed, it turns out that model theory and module theory fit together very well and almost all my work has combined models, modules and abelian categories in varying proportions.
My recent work has been mostly algebraic (though influenced by and sometimes motivated by model theory) and has centred around the Ziegler spectrum, in general and in the context of representations of finite-dimensional algebras. I have just finished writing a book on all this.
Recently I have become very interested in "geometric representation theory / non-commutative geometry" (e.g. module varieties, motivic methods) but, as well as these new directions, I continue to work on various of the many open problems around Ziegler spectra (and finite-dimensional algebras) and to push forward a programme to develop functorial model theory.
Back to the school homepage.