Abstract:
In this paper I will analyze the conditions under which pragmatism was received and interpreted in Germany. More precisely, I will try to highlight the conditions and main characteristics sustained by the early interpretation of pragmatism in Germany, interpretation that had created the conditions of reception for the Frankfurt School and, specially, for Max Horkheimer in his “Eclipse of Reason”. An approach to the works of John Dewey and Max Horkheimer will be crucial to the objectives, and the contributions of Hans Joas related to the relation between pragmatism and Critical Theory will be addressed as a primary reference. Finally, I will argue that a sort of democratic experimentalism comes in the Deweyan democratic pragmatism as a form of ethical, moral and political anti-fundamentalism with meaningful significance in contemporary democratic practices.

Abstract:
In this paper we introduce and study the notion of dynamical forcing. Basically, we develop a toolkit of techniques to produce finitely presented groups which can only act on the circle with certain prescribed dynamical properties. As an application, we show that the set X of rotation numbers which can be forced by finitely presented groups is an infinitely generated Q-module, containing countably infinitely many algebraically independent transcendental numbers. We also show that the set of subsets of the circle which are the set of rotation numbers of an element g of a group G under all actions of G on a circle, as G varies over all countable groups, are exactly the set of closed subsets of the circle which contain 0, and are invariant under the involution which interchanges x and -x. As another application, we construct a finitely generated group which acts faithfully on the circle, but which does not admit any faithful C^1 action, thus answering in the negative a question of John Franks.

Abstract:
We show that if M is a hyperbolic 3-manifold which admits a quasigeodesic flow, then pi_1(M) acts faithfully on a universal circle by homeomorphisms, and preserves a pair of invariant laminations of this circle. As a corollary, we show that the Thurston norm can be characterized by quasigeodesic flows, thereby generalizing a theorem of Mosher, and we give the first example of a closed hyperbolic 3-manifold without a quasigeodesic flow, answering a long-standing question of Thurston.

Abstract:
If P is an algebraic point on a commutative group scheme A/K, then P is _almost_rational_ if no two non-trivial Galois conjugates sigma(P), tau(P), have sum equal to 2P. In this paper, we classify almost rational torsion points on semistable elliptic curves over Q.

Abstract:
Modular Galois representations into GL_2(F_p) with cyclotomic determinant arise from elliptic curves for p = 2,3,5. We show (by constructing explicit examples) that such elliptic curves cannot be chosen to have conductor as small as possible at all primes other than p. Our proof involves finding all elliptic curves of conductor 85779, a custom computation carried out for us by Cremona. This leads to a counterexample to a conjecture of Lario and Rio. For p > 5, we construct irreducible representations with cyclotomic determinant that do not arise from any elliptic curve over Q.

Abstract:
We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we determine (using the theory of Breuil modules) when two finite flat group schemes G and H of order p over an arbitrarily tamely ramified discrete valuation ring admit an extension not killed by p.

Abstract:
We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over Q with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer--Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over Q with good reduction outside primes dividing N precisely when N is not in the set {1,2,3,5,6,7,10,13}.

Abstract:
Let T denote Thompson's group of piecewise 2-adic linear homeomorphisms of the circle. Ghys and Sergiescu showed that the rotation number of every element of T is rational, but their proof is very indirect. We give here a short, direct proof using train tracks, which generalizes to PL homeomorphism of the circle with rational break points and derivatives which are powers of some fixed integer, and also to certain flows on surfaces which we call "Thompson-like". We also obtain an explicit upper bound on the smallest period of a fixed point in terms of data which can be read off from the combinatorics of the homeomorphism

Abstract:
This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive e there is a positive d depending only on n and on e such that an element of pi_1(M) with stable commutator length less than d is represented by a geodesic with length less than e. Moreover, for any such M, the first accumulation point for stable commutator length on conjugacy classes is at least 1/12. Conversely, "most" short geodesics in hyperbolic 3-manifolds have arbitrarily small stable commutator length. Thus stable commutator length is typically good at detecting the thick-thin decomposition of M, and 1/12 can be thought of as a kind of homological Margulis constant.