![]() #Hausdorff dimension subshift angle doubling freeLet $F$ be a free group with rank at least 2. We will go on to talk about a new definition which has arisen from a generalisation of Benjamin-Schram graph convergence and, time allowing, it connections to an old conjecture of Remesselenikov to do with the genus of free groups.Īsymptotics comparing length functions on free groups In this talk we will explore different definitions of finiteness conditions for infinite groups discussing their connections to each other and geometric interpretations. I will explain the general theory before discussing various versions of a Proper Mapping Theorem for coadmissible D-modules, in particular showing that the functors in our Beilinson-Bernstein equivalence preserve coadmissibility. In this setting, the notion of coherence gets naturally replaced by that of 'coadmissibility'. Ardakov and Wadsley have begun to develop a theory of D-modules on rigid analytic spaces in the sense of Tate, hoping for analogous results in a p-adic locally analytic setting. The Beilinson-Bernstein localization allows us to study representations of Lie algebras geometrically, as D-modules on the associated flag variety. Efficient position can be understood as some kind of general position for curves on surfaces with respect to train tracks and I intend to address the question of its existence as well as discuss possible applications.Ĭoadmissible D-modules on rigid analytic flag varieties After giving relevant background material and elaborating on the interplay between train tracks and curves on surfaces, I plan to define the notion of efficient position of curves with respect to train tracks. Train tracks were introduced by Thurston in the late 1970s as a combinatorial tool for studying surface diffeomorphisms. Train tracks, curves and efficient position Key words are Mayer-Vietoris, product structures, functoriality and group extensions. I will try to make it accessible by comparing the tools and results of bounded cohomology to their well understood counterparts in classical cohomology. It has very exotic and unexpected behaviour. The bounded cohomology of groups was promoted by Gromov in the 80s to attack rigidity questions. ![]()
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