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 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 various important classes of algebras. 

I am currently working on several projects concerning Koszul algebras and symmetric special biserial algebras which study the structure of the Ext algebra, the Hochschild cohomology ring, and support varieties for modules as well as the consequent representation-theoretic information this yields. 

Current PhD students: Joanne Leader (started October 2010)

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 2012.

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 2011/2012, I am teaching MA3101 Irreducible Polynomials and Squaring the Circle (semester 1) and MA3511 Communicating Mathematics (semester 2).

Outreach Events

• Departmental contact for Undergraduate Ambassador Scheme (UAS)
• Maths/PGCE Alumni lunch: 23rd February 2011
• Year 10 Masterclasses: Saturday 25th June and Saturday 9th July 2011
• G-STeM Conference for year 12 students: Tuesday 28th June 2011
  Mathematical topics: Infinity; Learning mathematics through games and puzzles; Euler's gem or How many pentagons are there on a football?; Continued fractions.