A Thompson Group for the Basilica

We describe a Thompson-like group of homeomorphisms of the Basilica Julia set. Each element of this group acts as a piecewise-linear homeomorphism of the unit circle that preserves the invariant lamination for the Basilica. We develop an analogue of tree pair diagrams for this group which we call arc pair diagrams, and we use these diagrams to prove that the group is finitely generated. We also prove that the group is virtually simple.Comment: 23 pages, 31 figure

Rearrangement Groups of Fractals

We construct rearrangement groups for edge replacement systems, an infinite class of groups that generalize Richard Thompson's groups F, T, and V . Rearrangement groups act by piecewise-defined homeomorphisms on many self-similar topological spaces, among them the Vicsek fractal and many Julia sets. We show that every rearrangement group acts properly on a locally finite CAT(0) cubical complex, and we use this action to prove that certain rearrangement groups are of type F infinity.Comment: 48 pages, 37 figure

From Mathematical Fictionalism to Truth‐Theoretic Fictionalism

We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism

Funding, school specialisation and test scores:an evaluation of the specialist schools policy using matching models

We evaluate the effect on test scores of a UK education reform which has increased funding of schools and encouraged their specialisation in particular subject areas, enhancing pupil choice and competition between schools. Using several data sets, we apply cross-sectional and difference-in-differences matching models, to confront issues of the choice of an appropriate control group and different forms of selection bias. We demonstrate a statistically significant causal effect of the specialist schools policy on test score outcomes. The duration of specialisation matters, and we consistently find that the longer a school has been specialist the larger is the impact on test scores. We finally disentangle the funding effect from a specialisation effect, and the latter occurs yielding relatively large improvements in test scores in particular subjects

The Market Reaction to Legal Shocks and Their Antidotes: Lessons from the Sovereign Debt Market

In October 2000 a hedge fund holding an unpaid debt claim won an enormous victory against the debtor, the Republic of Peru, through an opportunistic interpretation of the common pari passu clause by a Brussels court. This development was met by charges from policy makers and practitioners that the court\u27s decision (its novel interpretation of the pari passu clause) would lead to a dramatic increase in the risks of holdout litigation faced by sovereign debtors. Over the ensuing years, multiple reform solutions were proposed including the revision of certain contractual terms, the filing of amicus briefs in a key case, and the imposition of an international bankruptcy regime for sovereigns. The question, looking back, that this Article empirically investigates is whether the capital markets actually perceived a significant increase in risk at the time of the October 2000 Brussels court decision. Equally important is whether markets discriminate among competing versions of the pari passu clause based on their relative risks for holdouts. And, to the extent the markets did react to the increase in legal risk, did any of the antidotes that were implemented to reduce the supposed increased holdout risk work? We offer evidence that bond prices did respond to this legal shock, that markets do discriminate based on the relative holdout risk posed by differing forms of the pari passu clause, and provide surprising evidence regarding the efficacy of the government-sponsored antidote, the advent of collective action clauses