\author{David J. Benson}
\address{Institute of Mathematics \\ University of Aberdeen \\ Aberdeen AB24 3UE \\ UK}
\title{Modules for elementary abelian groups and hypersurface singularities}
\thanks{This material is based upon work supported by the National Science 
Foundation under Grant No. 0932078~000, while the author was in 
residence at the Mathematical Science Research Institute (MSRI) in 
Berkeley, California, during the Spring semester of 2013.} 

\begin{document}

\maketitle
\begin{abstract}
This paper is an expanded version of the lecture I gave at
the conference on ``Representation Theory, Homological Algebra
and Free Resolutions'' at MSRI in February 2013. My goals
in this lecture were to explain to an audience of commutative
algebraists why a finite group representation theorist might
be interested in zero dimensional complete intersections, and to give 
a version of the Orlov correspondence in this context that is
well suited to computation. In the context of modular representation
theory, this gives an equivalence between the derived category
of an elementary abelian $p$-group of rank $r$, and the category of
(graded) reduced matrix factorisations of the polynomial 
$y_1X_1^p+\dots+y_rX_r^p$.
Finally, I explain the relevance to
some recent joint work with Julia Pevtsova on realisation of
vector bundles on projective space from modular representations
of constant Jordan type.
\end{abstract}