The purpose of the present paper is to expose, in substantial detail, certain remarkable similarities between inter-universal Teichmüller theory and the theory surrounding Bogomolov’s proof of the geometric version of the Szpiro Conjecture. These similarities are, in some sense, consequences the fact that both theories are closely related to the hyperbolic geometry of the classical upper half-p...

The purpose of the present paper is to expose, in substantial detail, certain remarkable similarities between inter-universal Teichmüller theory and the theory surrounding Bogomolov’s proof of the geometric version of the Szpiro Conjecture. These similarities are, in some sense, consequences the fact that both theories are closely related to the hyperbolic geometry of the classical upper half-p...

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories, classical topological field theories – whose classical solutions span topological classes of manifolds – and reparametri-sation invariant theories – gener...

Theories of counterfactuals agree on appealing to a relation comparative similarity, but disagree the quantificational force counterfactuals. We report two experiments testing predictions three main approaches: universal theories, homogeneity and single-world selection theories (plus supervaluations over functions). The critical cases in our experiment were constructed so as discriminate betwee...