The Role of the IMF in Future Sovereign Debt Restructurings: Report of the Annenberg House Expert Group

A meeting of international finance and insolvency experts was held on November 2, 2013 at the Annenberg House in Santa Monica, California. The meeting was co-hosted by the USC Law School and the Annenberg Retreat at Sunnylands. The goal was to solicit the views of experts on the implications of the IMF’s April 26, 2013 paper captioned “Sovereign Debt Restructuring -- Recent Developments and Implications for the Fund’s Legal and Policy Framework”. The April 26 paper may signal a shift in IMF policies in the area of sovereign debt workouts. Although the Expert Group discussed a number of the ideas contained in the April 26 paper, attention focused on paragraph 32 of that paper. That paragraph states in relevant part: “There may be a case for exploring additional ways to limit the risk that Fund resources will simply be used to bail out private creditors. For example, a presumption could be established that some form of a creditor bail-in measure would be implemented as a condition for Fund lending in cases where, although no clear-cut determination has been made that the debt is unsustainable, the member has lost market access and prospects for regaining market access are uncertain.” This Report summarizes the consensus views of the Expert Group on the practical implications of the suggestions contained in paragraph 32 of the April 26 paper

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Willmore Surfaces of Constant Moebius Curvature

We study Willmore surfaces of constant Moebius curvature $K$ in $S^4$. It is proved that such a surface in $S^3$ must be part of a minimal surface in $R^3$ or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in $S^4$ of constant $K$ could only be part of a complex curve in $C^2\cong R^4$ or the Veronese 2-sphere in $S^4$. It is conjectured that they are the only examples possible. The main ingredients of the proofs are over-determined systems and isoparametric functions.Comment: 16 pages. Mistakes occured in the proof to the main theorem (Thm 3.6) has been correcte

The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes

The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.Comment: 12 pages, 2 figures, strongly extended versio