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

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

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

Аннотация курса