Balanced Cayley complexes and MDS codes

Cayley graphs play an important role in various mathematical areas, and in recent years there is an interest in studying high dimensional versions of these graphs. In this talk we will focus on one such extension, called Balanced Cayley Complexes (BCC). In particular, we'll discuss:

1. A Fourier approach to the homology of BCC's over prime fields, with applications to the construction of hypertrees and MDS codes.
Joint work with Gilles Zemor.

2. Lower bounds on the spectral gaps of the higher Laplacians of a BCC and a high dimensional version of the Alon-Roichman theorem.