Scheme: Wolfson Research Merit Awards
Organisation: Imperial College London
Dates: Aug 2010-Jul 2015
Summary: This year I mainly studied "derived categories of coherent sheaves". These are abstract algebraic gadgets that encode a lot of information about geometry. However they do not contain all information, so two different geometries can give rise to the same derived category. Examples of this phenomenon are still rather rare, and we employed a general method (Kuznetsov's "homological projective duality") to produce new examples.
This work is a long way from applications in the real world! But in the unreal world of "string theory" in theoretical physics, they give examples of "the category of boundary conditions in B-twisted topological string theory".
Scheme: University Research Fellowship
Dates: Oct 2000-Sep 2008
Summary: This project summary is not available for publication.