Title: A Tale of Two Dualities

Jean Goubault-Larrecq
       (LSV/ENS Cachan & CNRS UMR 8643 & INRIA projet SECSI)

Abstract: 
	Stably compact spaces enjoy a wonderful mathematical duality,
	put forward as early as 1948 by Leopoldo Nachbin in his study
	of compact pospaces, and which we shall call de Groot
	duality. This has been discovered as particularly relevant to
	domain theory by A. Jung and others in the 1990s. Let us say
	that any coherent domain is stably compact, and these include
	Scott domains, Plotkin's retracts of bifinite domains, and
	Jung's FS-domains. 
                    Although I never quite stressed it, a
	running thread of the research I have been conducting in the
	last few years on modeling mixed non-determinism and
	probabilistic choice is another, related duality which I
	called convex-concave duality. 
                     To put it in a mysterious way,
	the latter says that you may trade good for evil, angels for
	demons, sups for mins, depending on your point of view.  
                    The point of the talk will be to explain intuitions behind
	this, how this translates mathematically on several models of 
	mixed non-determinism and probabilistic choice, and how this
	is used to get two theorems from just one proof, in several
        instances.