Singularity dominated strong fluctuations for some random matrix averages

The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval $(0,1)$ of the real line respectively. The averaged value of the modulus of the corresponding characteristic polynomial raised to the power $2 \mu$ diverges, for $2\mu \le -1$, at points approaching the eigenvalue support. Using the theory of generalized hypergeometric functions based on Jack polynomials, the functional form of the leading asymptotic behaviour is established rigorously. In the circular ensemble case this confirms a conjecture of Berry and Keating.Comment: 11 pages, to appear Commun. Math. Phy

Lagrangian tori in four-dimensional Milnor fibres

The Milnor fibre of any isolated hypersurface singularity contains many exact Lagrangian spheres: the vanishing cycles associated to a Morsification of the singularity. Moreover, for simple singularities, it is known that the only possible exact Lagrangians are spheres. We construct exact Lagrangian tori in the Milnor fibres of all non-simple singularities of real dimension four. This gives examples of Milnor fibres whose Fukaya categories are not generated by vanishing cycles. Also, this allows progress towards mirror symmetry for unimodal singularities, which are one level of complexity up from the simple ones.Comment: v2: 66 pages, 37 figures; minor change

Wintenberger's Functor for Abelian Extensions

Let $k$ be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian $p$-adic Lie extensions $E/F$, where $F$ is a local field with residue field $k$, and a category whose objects are pairs $(K,A)$, where $K\cong k((T))$ and $A$ is an abelian $p$-adic Lie subgroup of \Aut_k(K). In this paper we extend this equivalence to allow \Gal(E/F) and $A$ to be arbitrary abelian pro-$p$ groups.Comment: 12 page

Rethinking Sovereignty : Independence-lite, devolution-max and national accommodation

Peer reviewedPublisher PD

Brexit and Devolution in the United Kingdom

This work was carried out as part of the UK in a Changing Europe programme of the Economic and Social Research Council.Peer reviewedPublisher PD

Is it Time to Address Selective Disclosure for Nonprofit Organizations?

Over the past two decades, there have been several highly publicized nonprofit scandals that have eroded the publics confidence in the sector (Aviv 2004). Significant changes in nonprofit regulation have been implemented to address these concerns that have expanded the financial information available to the public. Interestingly, the calls for more nonprofit accountability have not focused on an important concern, that of selective disclosure. This is a practice under which an organization provides material information to some constituents while withholding it from others. This paper argues that practice is frequently observed in the nonprofit sector. As the New Era Philanthropy scandal highlighted, this practice can pose substantial risks to the nonprofit sector by facilitating fraud and harming the publics trust. The paper describes the existing nonprofit reporting requirements and potential shortcomings. It examines two alternative disclosure environments, the Freedom of Information Act (FOIA) in the federal government and corporate securities regulation, particularly Regulation Fair Disclosure, and their limitations. It will then discuss what measures could be taken to address selective disclosure in the nonprofit sector.This publication is Hauser Center Working Paper No. 33.7. Hauser Working Paper Series Nos. 33.1-33.9 were prepared as background papers for the Nonprofit Governance and Accountability Symposium October 3-4, 2006