Dirac spectra, summation formulae, and the spectral action

Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Concerted action for successful coastal communities in Tanzania: Lessons from the Tanzania Coastal Management Partnership (TCMP) 2006-2009

The Tanzania Coastal Management Partnership (TCMP) works to implement the National Integrated Coastal Environmental Management Strategy (ICEMS) in Tanzania’s coastal landscapes and seascapes, funded in large measure by the U.S. Agency for International Development. The overarching goal of the Sustainable Coastal Communities and Ecosystems in Tanzania (SUCCESS Tanzania) initiative is to conserve coastal and marine biodiversity while improving the well being of coastal residents through implementation of the Tanzania ICEMS and related ICM policies and strategies. It does this by focusing on three key results: -Policies and Laws that Integrate Conservation and Development Applied -Participatory Landscape Scale Conservation Practiced -Conservation Enterprises Generate Increased and Equitable Benefits from Sustainable Use An additional result sought in the program is gender equity and HIV/AIDS preventive behaviors promoted through communicating HIV/AIDS, environment, and equity messages. (PDF contains 3 pages)

Implications of governance structures on urban climate action: evidence from Italy and Spain

47 p.

Pond action: Promoting the conservation of ponds in Britain

Pond Action is an independent freshwater conservation project which was started in 1987. It is based in the School of Biological and Molecular Sciences in Oxford Polytechnic and has five full-time staff with two senior advisors. The main aim of Pond Action's work has been to promote the conservation of ponds by creating a sound, scientific basis for pond conservation. An essential aspect of this work is the need to make the results of scientific work available and understandable to everybody concerned with pond conservation.