As a concrete example I'll cast Latent Semantic Indexing (LSI, which I'll explain) in the framework and demonstrate its inherent theoretical and practical difficulties with ambiguous terms (so-called polysems). Furthermore, the framework leads to an efficient implementation with query processing time proportional to the number of query terms (and not the number of latent dimensions as in standard implementations).
I might mention other benefits (analysis of PLSI, applications to peer-2-peer retrieval, top-k retrieval for concept-based techniques) but will not discuss these in detail.
The most advanced bit of mathematics I'll use will be the linearity of the scalar product. If this doesn't scare you then you should come.
This talk is based on joint work with Holger Bast.
More details can be found at:
www.mpi-sb.mpg.de/~iweber/framework/framework.pdf