Abstract: We will discuss some recent results concerning order preserving and order reversing transforms on convex bodies and functions. We will see a new duality transform on geometric convex functions, and how it is a special case of fractional-linearity. We will discuss variants of the fundamental theorem of affine geometry. If time permits, we will also discuss how the chain rule characterizes the derivative and how exchanging convolution with product characterizes the Fourier transform. Based on joint works with V. Milman, S. Alesker, D. Faifman, D. Florentin, H. Konig and B. Slomka.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006