We shall review the Chern-Weil theory cast in the language of finitely generated projective modules. This algebraic approach has the advantage that it can be extended to noncommutative settings.

Convexity has played an important role in the development of the theory of several complex variables. In this first of a series of talks, I will give a brief introduction to the various notions of convexity that complex analysts have found useful. We will then define an (equi)affine-invariant surface area measure for convex bodies, and discuss some related problems.The subsequent talk(s) will focus on its relatively less explored complex analog --- the Fefferman hypersurface area measure. This talk will be accessible to graduate students.