11. April 2024, 15:30 until 17:00
AKOR Seminar: Characterizing order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond.. via inf/sup irreducibility, Pierre-Cyril Aubin, TU Wien
There has been many parallel streams of research studying order isomorphisms of some specific sets G of functions over a set X, such as convex or Lipschitz functions. I will give in this talk a unified abstract approach inspired by c-convex functions. The results are obtained highlighting the role of inf and sup-irreducible elements of G and the usefulness of characterizing them, to subsequently derive the structure of order isomorphisms, and in particular of those commuting with the addition of scalars. You will see that in many cases all the (max,+)-isomorphisms J:G->G are of the form Jf=g+f\circ \phi with g:X->R and \phi:X->X bijective. We apply our theory to the sets of c-convex functions on compact Hausdorff spaces, to the set of lower semicontinuous (convex) functions on a Hausdorff topological vector space and to Lipschitz and 1-Lipschitz functions of (weak) metric spaces with compact balls. We encompass in this way many results of Artstein-Avidan and Milman, Sanchéz and Sanchéz, Leung, and others. This is a joint work with Stéphane Gaubert (INRIA, France).

Please note start time 15:30!