Geometric Study of Convex and Quasi-concave Functions in R^n

We will discuss three subjects which, as we will see, are staringly connected:

1. Duality and new structures on the family of convex (and logconcave) functions in R^n.
2. Classical constructions in Analysis which appear (uniquely) from elementary (simplest) properties.
3. Extension of Minkowski polarization result to log-concave and quasi-concave functions; Mixed integrals. 

Аннотация курса