Let No be Conway’s class of surreal numbers. I will make explicit the notion of a function f on No recursively defined over some family of functions. Under some ‘tameness’ and uniformity conditions, f must satisfy some interesting properties; in particular, the supremum of the class ̆ x ∈ No : f (x) ≥ 0 ̄ is actually an element of No. As an application, I will prove that concatenation function x ...

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of cliques that occur as (topological) r-minors. We observe that this tameness notion from algorithmic graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence pr...

In his 1986 article [Th2], W. Thurston proposed that one might approachMarden’s conjecture from a dynamical point of view via a study of limits in the natural deformation space: its interior consists of geometrically finite manifolds, and promoting their tameness to algebraic limits on the boundary has proven to be a successful strategy to address Marden’s conjecture in special cases. In this p...

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension G̃ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for G̃ and its applications to the study of Hecke algebras via a Satake is...

Abstract. In [7], the second author classified configurations of the singularities on tame sextics of torus type. In this paper, we give a complete classification of the singularities on irreducible sextics of torus type, without assuming the tameness of the sextics. We show that there exists 121 configurations and there are 5 pairs and a triple of configurations for which the corresponding mod...