Asymptotic Geometric Analysis Seminar

Fall-Winter Semester, 2012-13.

Sunday, 13:10-15:00, Schreiber - room 209

21.10 Introductory meeting

28.10 B. Slomka Gaussian random variables, Sudakov’s inequality, Dudley and more.

4.11 L. Rotem On a generalization of Mixed Volumes for some classes of functions.

11.11 D. Florentin Kahane Kchintchine inequalities and related topics

18.11 R. Eldan Isoperimetric problems for convex bodies

25.11 R. Eldan More on isoperimetric problems for convex bodies

2.12 K. Gutmen-Einhorn Busemann’s inequality

9.12 Happy Hannuka

16.12 D. Ryabogin, On non-uniqueness of convex bodies with prescribed volumes of sections and projections.

and

B. Vritsiou, Geometry of convex bodies with maximal isotropic constant.

23.12 A. Livne, Dvoretzky’s theorem

and

Y. Rozenshein, The critical dimension for l_q

30.12 A. Segal, Isomorphic Steiner symmetrization of p-convex sets

6.1 cancelled due to Paris

13.1 Y. Nir Relations between billiard orbits and other geometric properties

20.1 Short talks by : Y. Shelah, O. Cohen-Alloro, E. Udassin and Boris Landa [Last meeting of the semester]

We shall have an extra meeting after the semester ends, with a guest speaker from IMPA, Rio de Janeiro

3.2 Daniel Reem, Order preserving and order reversing operators on the class of convex functions in Banach spaces
ABSTRACT:
Recently S. Artstein-Avidan and V. Milman have developed an abstract duality theory and proved the following remarkable result: up to linear terms, the only  fully order preserving operator (namely, an invertible operator whose inverse also preserves  the point-wise order between functions) acting on the class of lower semi continuous proper convex functions defined on Rn is the identity operator, and the only fully order reversing operator acting on the same set is the  Fenchel conjugation (Legendre transform). We establish a suitable extension of their result to infinite dimensional Banach spaces. This is a joint work with Alfredo N. Iusem and Benar F. Svaiter