Abstract: 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.

Abstract:

Abstract: 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.