Professor in Pure Mathematics

tel: +44 (0) 116 252 3888
email: njs5(at)mcs.le.ac.uk 

Research

My research is in the representation theory of algebras, in the study of Hochschild cohomology of finite-dimensional algebras.

In joint work with Oeyvind Solberg (Trondheim), I used Hochschild cohomology to develop a theory of support varieties for a finitely generated module over an artin algebra. Subsequent work of ours with Karin Erdmann (Oxford), Miles Holloway (Oxford) and Rachel Taillefer (St Etienne) has concentrated on support varieties for selfinjective algebras. Finiteness conditions play an important role in this theory, including the question of when, for a finite-dimensional algebra over an algebraically closed field, the Hochschild cohomology ring modulo nilpotence is finitely generated as an algebra. The Hochschild cohomology ring modulo nilpotence has been shown to be finitely generated for several classes of algebras, in joint projects with Edward Green (VPI & SU, Virginia), Oeyvind Solberg, Rachel Taillefer. Current projects in Koszul algebras and in symmetric special biserial algebras continue to study the structure of the Ext algebra, the Hochschild cohomology ring, and support varieties for modules. 

Current PhD students: Ahlam Fallatah. 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.

Slides for talks at "Symposium on ring theory and representation theory", Shizuoka University, Japan, September 2008.

For more information see my RESEARCH PAPERS.

BLOC

I am a joint organiser of BLOC, the Bristol Leicester Oxford 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.

Teaching

In the first semester, I am on study leave. In the second semester, I am teaching MA1271 Geometry of the Plane.

Administration

I am chair of the departmental outreach committee and coordinate the outreach activities of the department. I am also the departmental contact for the Undergraduate Ambassadors Scheme (UAS).