Dilemmas and Trade-Offs in Peacemaking: A Framework for Navigating Difficult Decisions

This article focuses on the dilemmas and trade-offs that third parties face when mediating violent political conflicts. Should they ignore human rights violations because pushing the issue could jeopardize relationships with political actors who grant access for humanitarian aid? Will bringing moderates and hardliners together help the peace process or radicalize moderate actors? What should dialogue facilitators do when the act of identifying non-mainstream groups to be included into dialogue increases division and polarization? The activity of peacemaking is inherently characterized by such process and strategy dilemmas where two equally compulsory imperatives seem not to be attainable at the same time. The article proposes a framework to break out of either-or thinking in these situations. We argue that: 1) making oneself aware of how a decision is perceived, and 2) systematically exploring a set of different strategies for creating new unexpected options helps to ease these decisions and avoid rotten compromises. The model reworks and combines existing problem-solving strategies to create a new explorative option generation approach to peacemaking dilemmas and trade-offs. Some of these strategies, such as sequencing and incrementalization, are already well-established in peacemaking. Others, such as compartmentalization and utilization, are rather unconsciously used. All identified strategies, however, are not yet systematically employed to manage third parties’ own dilemmas and trade-offs. Under the suggested framework, these strategies can act in complement to synthesize creativity and strategic thinking with surprising ease. Using examples from the authors’ peacemaking activities and observations in Myanmar, Thailand, and Ukraine, the article demonstrates the real-world benefits of the framework in terms of decision assessment and optional thinking

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series

The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139

Sub-Riemannian Calculus on Hypersurfaces in Carnot Groups

We develope basic geometric quantities and properties of hypersurfaces in Carnot groups

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Dimension rigidity in conformal structures

Let $\Lambda$ be the limit set of a conformal dynamical system, i.e. a Kleinian group acting on either finite- or infinite-dimensional real Hilbert space, a conformal iterated function system, or a rational function. We give an easily expressible sufficient condition, requiring that the limit set is not too much bigger than the radial limit set, for the following dichotomy: $\Lambda$ is either a real-analytic manifold or a fractal in the sense of Mandelbrot (i.e. its Hausdorff dimension is strictly greater than its topological dimension). Our primary focus is on the infinite-dimensional case. An important component of the strategy of our proof comes from the rectifiability techniques of Mayer and Urba\'nski ('03), who obtained a dimension rigidity result for conformal iterated function systems (including those with infinite alphabets). In order to handle the infinite dimensional case, both for Kleinian groups and for iterated function systems, we introduce the notion of pseudorectifiability, a variant of rectifiability, and develop a theory around this notion similar to the theory of rectifiable sets. Our approach also extends existing results in the finite-dimensional case, where it unifies the realms of Kleinian groups, conformal iterated function systems, and rational functions. For Kleinian groups, we improve on the rigidity result of Kapovich ('09) by substantially weakening its hypothesis of geometrical finiteness. Moreover, our proof, based on rectifiability, is entirely different than that of Kapovich, which depends on homological algebra. Another advantage of our approach is that it allows us to use the "demension" of \v{S}tan$'$ko ('69) as a substitute for topological dimension. For example, we prove that any dynamically defined version of Antoine's necklace must have Hausdorff dimension strictly greater than 1 (i.e. the demension of Antoine's necklace)

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket

An open toolkit for tracking open science partnership implementation and impact.

Serious concerns about the way research is organized collectively are increasingly being raised. They include the escalating costs of research and lower research productivity, low public trust in researchers to report the truth, lack of diversity, poor community engagement, ethical concerns over research practices, and irreproducibility. Open science (OS) collaborations comprise of a set of practices including open access publication, open data sharing and the absence of restrictive intellectual property rights with which institutions, firms, governments and communities are experimenting in order to overcome these concerns. We gathered two groups of international representatives from a large variety of stakeholders to construct a toolkit to guide and facilitate data collection about OS and non-OS collaborations. Ultimately, the toolkit will be used to assess and study the impact of OS collaborations on research and innovation. The toolkit contains the following four elements: 1) an annual report form of quantitative data to be completed by OS partnership administrators; 2) a series of semi-structured interview guides of stakeholders; 3) a survey form of participants in OS collaborations; and 4) a set of other quantitative measures best collected by other organizations, such as research foundations and governmental or intergovernmental agencies. We opened our toolkit to community comment and input. We present the resulting toolkit for use by government and philanthropic grantors, institutions, researchers and community organizations with the aim of measuring the implementation and impact of OS partnership across these organizations. We invite these and other stakeholders to not only measure, but to share the resulting data so that social scientists and policy makers can analyse the data across projects