To any graph, one may associate three flavors of hyperplane arrangements: linear (subspaces of a complex vector space), toric (subtori of a complex torus), or abelian (abelian subvarieties of a complex abelian variety). In the linear case, there is considerable literature on the rational homotopy theory of the complement, and the toric case is similar in flavor. The abelian case is more complicated due to lack of formality of the space. When the graph is chordal, we have a Koszul model and use quadratic-linear duality to compute the minimal model and show that the space is rationally $K(\pi,1)$. This is joint work with Justin Hilburn.

In the first part, we continue with the following topics: ---Clifford algebras, Clifford modules, spin structures, Dirac operators, Weitzenbock formula. ---Heat kernel and its asymptotic expansion, Gilkey's formula, McKean-Singer formula.

In the second part, Mitsuru Wilson (Western) will continue developing the theory of Hilbert C*-modules and discuss the KSGNS construction.