Abstract: The geometric part of this talk will be mostly a "hand-waving" discussion on some very recent and, I believe, very surprising results (all in collaboration with Shiri Artstein-Avidan), and on most of which Shiri gave a colloquium a year ago. To get the flavor of the analytic part, please try to give sense to the following statements (which only sounds metamathematical):

(i) Derivation on C^1 functions is a "regularized" logarithm of the product;
(ii) The second derivative is a "regularized" logarithm of the first derivative;
(iii) The entropy function is the derivation on C(R) (i.e. the only derivation).
(The last statement is the easiest, which one may try to understand before my talk.)

The analytic part is joint with Hermann Konig, but has a piece also joint with Shiri Artstein.

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