Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics

We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalar-flat Kahler metrics and hypercomplex structures with symmetry. We also show that in the presence of such a congruence, the Einstein-Weyl equation is equivalent to a pair of coupled monopole equations, and we solve these equations in a special case. The new Einstein-Weyl spaces, which we call Einstein-Weyl ``with a geodesic symmetry'', give rise to hypercomplex structures with two commuting triholomorphic vector fields.Comment: 30 pages, 7 figures, to appear in Ann. Inst. Fourier. 50 (2000

On the nonlinear statistics of range image patches

In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp. 1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region. In this paper, we apply the techniques of Carlsson et al. to range patches. By enlarging to 5×5 and 7×7 patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen, and Mumford

Completely contractive projections on operator algebras

The main goal of this paper is to find operator algebra variants of certain deep results of Stormer, Friedman and Russo, Choi and Effros, Effros and Stormer, Robertson and Youngson, Youngson, and others, concerning projections on C*-algebras and their ranges. (See papers of these authors referenced in the bibliography.) In particular we investigate the `bicontractive projection problem' and related questions in the category of operator algebras. To do this, we will add the ingredient of `real positivity' from recent papers of the first author with Read.Comment: To appear Pacific J Math; several corrections and small improvements. Keywords Operator algebra, completely contractive map, projection, conditional expectation, bicontractive projection, real positive, noncommutative Banach-Stone theore

Real impact is about influence, meaning and value: Mapping contributions for a new impact agenda in the humanities.

The humanities are driven both by epistemological and normative interests in a range of topics resulting in a complex topography of the public value of the humanities. But for the most part, its diffuse knowledge and impact has been defined and restricted to inputs and outputs. David Budtz Pedersen presents an overview of a research project aiming to reveal the pathways of humanities research deeply integrated in the functioning and affluence of modern liberal societies

Overhyped and concentrated investments in research funding are leading to unsustainable science bubbles.

David Budtz Pedersen examines how the scientific market exhibits bubble behaviour similar to that of financial markets. Taking as an example the overwhelming investments in neuroscience, such high expectations may actually drain the research system from resources and new ideas. In the end the permanent competition for funding and the lack of ‘risk diversification’, might generate a climate in which citizens and policymakers lose their confidence in science as they did with the financial sector after the 2008 crash