Graph complexes, homology of the general linear group, and numbers
This talk will be a guided tour of some very distinct, but highly interconnected areas of combinatorics, algebraic geometry and number theory.
Graph complexes were introduced by Kontsevich and encode the contraction of edges in a graph. Despite the elementary definition, their homology is surprisingly
complicated and mostly unknown. After surveying recent results in this area, I will turn to the homology of the special linear group, and discuss the classical work of Minkowski on values of the zeta function, Voronoi on quadratic forms, and of Borel on stable cohomology.
In the final part of the talk I will try to draw the different strands together, and explain how these topics all share a common underlying pattern.