We'll continue to look at physical models coming from gauge theory. Starting from (parts of) the standard model as usual, followed by the NCG example of almost commutative manifolds and onto the goal of a gauge theory over a fuzzy'' manifold as in Perez-Sanchez.

This is our second talk about "nef" line bundles; this time it will be from the perspective of curvature. We will begin with a brief discussion of currents. This will lead into a discussion of curvature of line bundles, and a new definition of a nef line bundle. We will conclude by showing this new definition is equivalent to the old one.

By a cubic surface in $\mathbb{CP}^3$, we mean the zero set of a homogenous degree 3 polynomial in 4 variables. Cayley computed the number of lines on a 'generic' cubic surface to be 27. This number can be computed as the integral of the Euler class of a certain bundle over the Grassmannian $G(2, 4)$ of lines in $\mathbb{CP}^3$. To evaluate this integral, we observe that there is a certain action of 4-torus on $G(2, 4)$, and then we apply the Atiyah-Bott localization formula.