Professor in Pure Mathematics
tel: +44 (0) 116 252 3917
My research is in the representation theory of algebras, in the study of Hochschild cohomology of finite-dimensional algebras.
In joint work with O. Solberg, I used Hochschild cohomology to develop a theory of support varieties for a finitely generated module over an artin algebra. Subsequent work (with K. Erdmann, M. Holloway, O. Solberg and R. Taillefer) considered support varieties for selfinjective algebras, and showed, under certain reasonable finiteness conditions, that this theory is analogous to that of support varieties (as defined by group cohomology) for group algebras over finite groups.
Finiteness conditions play an important role, including the questions of when, for a finite-dimensional algebra over an algebraically closed field, the Hochschild cohomology ring, and/or the Hochschild cohomology ring modulo nilpotence, and/or the Ext algebra are finitely generated as algebras. Several joint projects have resulted in showing that the Hochschild cohomology ring modulo nilpotence is finitely generated as an algebra for many important classes of algebras. This yields information on the support varieties for modules as well as representation-theoretic information (such as representation type, Auslander-Reiten quiver).
My most recent projects study finite generation of the Ext algebra for Brauer graph algebras and generalisations of Koszul algebras.
For more information see my RESEARCH PAPERS.
Former PhD students:
Gabriel Davis, "Finiteness conditions on the Ext-algebra", completed 2005.
Deena Al-Kadi, "Self-injective algebras and the second Hochschild cohomology group", completed 2005.
Ahlam Fallatah, "Hochschild cohomology and periodicity of tame weakly symmetric algebras", completed 2011.
Joanne Leader, "Finite generation of Ext and (D,A)-stacked algebras", completed 2014.
I am a joint organiser of BLOC, the Bristol Leicester Oxford City Colloquium. This promotes collaborative work by research in the Representation Theory of Algebras through meetings and seminars and is supported by a London Mathematical Society scheme 3 grant.
Member of the steering committee of the EPSRC funded Anglo-French-German Representation Theory network.
HH4 - Fourth International Conference on Hochschild Cohomology: Structure and Applications, August 12 - 16, 2013, Universidad de Buenos Aires, Buenos Aires, Argentina.
Selected recent invitations: Virginia Tech, USA 2013, 2011, 2010; Clermont-Ferrand, France 2012; TUS, Tokyo, Japan 2010, St Etienne, France 2009; Shizuoka, Japan 2008.
I currently chair the Department's Self-Assessment Team for Athena SWAN and am the Departmental contact for the Undergraduate Ambassador Scheme (UAS) .