In April this year I’ll be giving a talk, with the title Candidate Betti numbers for the linear homology of convex polytopes. at the Universit√© Libre de Bruxelles. Here are Candidate Betti numbers for linear homology slides that I originally prepared.¬† And here’s the Finding linear homology slides that I’ll actually use for the seminar. The second set is short, and gets to the main definitions more quickly.¬† The first set puts the material in context, but is much too much for a single talk. [Second set of slides added April 1, 2013.]

Here’s the abstract:

The middle perversity intersection homology (mpih) Betti numbers of the toric variety associated with a convex polytope are linear functions of the flag vector of the convex polytope.
In this talk I define similar linear functions, which I hope are the Betti numbers for a not yet defined homology theory. This linear homology theory should exist wherever mpih does.
Such homology would prove that these candidate Betti numbers are actual Betti numbers, and so non-negative on all convex polytopes (being the dimension of a vector space).