Klaas Landsman:   The principle of general tovariance
 
Inspired by the work of Klaus Fredenhagen (notably his papers with Haag and with Brunetti & Verch on generally covariant quantum field theory) we propose a new principle of physics and especially quantum gravity. This principle states that physical laws should look the same in whatever topos they are defined (a topos is a generalization of the category of sets). This principle is related to the recent topos-theoretic approach to physics formulated by Isham & Doering, although the earlier explicit construction of quantum mechanics by Isham & Butterfield fails to satisfy it for technical reasons. Another source of inspiration has been recent work by Chris Heunen, Bas Spitters at Nijmegen. Finally, the speaker's own past work on the functoriality of quantization played a role, which principle should emerge as a special case of tovariance.
The talk contains an introduction to topos theory and will be comprehensible to any mathematical physicist who isn't afraid of categories and functors.