Number Theory Seminar: Cohomology of certain graph hypersurfaces and counting of rational points

I will speak about the cohomology of the middle degree of graph hypersurfaces of some special Feynman graphs, the "generalised zigzag" graphs, and about how to connect this to counting rational points of this hypersurfaces. Then I will explain, why "wheel with spokes" WSn are polynomially countable (in the spirit of Kontsevich conjecture), and will give an example of graph which is not polynomially countable. I will say some words about the number of points of gluing of graphs.