CURRENT PROGRAMS FOR MEETING SPECIAL EDUCATION AND TRAINING NEEDS - A REPORT

Teaching/Communication/Extension/Profession,

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Baryon Resonance Analysis from SAID

We discuss the analysis of data from piN elastic scattering and single pion photo- and electroproduction. The main focus is a study of low-lying non-strange baryon resonances. Here we concentrate on some difficulties associated with resonance identification, in particular the Roper and higher P11 states.Comment: 4 pages, 6 figures; Nstar2009 Conf Proceedings; small revisio

Topological complexity of the relative closure of a semi-Pfaffian couple

Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskii's Pfaffian functions. In this paper, use the notion of format (or complexity) of a Pfaffian couple to derive explicit upper-bounds for the homology of its relative closure. Keywords: Pfaffian functions, fewnomials, o-minimal structures, Betti numbers.Comment: 12 pages, 1 figure. v3: Proofs and bounds have been slightly improve

Survival and Home-range Size of Northern Spotted Owls in Southwestern Oregon

In the Klamath province of southwestern Oregon, Northern Spotted Owls (Strix occidentalis caurina) occur in complex, productive forests that historically supported frequent fires of variable severity. However, little is known about the relationships between Spotted Owl survival and home-range size and the characteristics of fire-prone, mixed-conifer forests of the Klamath province. Thus, the objectives of this study were to estimate monthly survival rates and home-range size in relation to habitat characteristics for Northern Spotted Owls in southwestern Oregon. Home-range size and survival of 15 Northern Spotted Owls was monitored using radiotelemetry in the Ashland Ranger District of the Rogue River–Siskiyou National Forest from September 2006 to October 2008. Habitat classes within Spotted Owl home ranges were characterized using a remote-sensed vegetation map of the study area. Estimates of monthly survival ranged from 0.89 to 1.0 and were positively correlated with the number of late-seral habitat patches and the amount of edge, and negatively correlated with the mean nearest neighbor distance between late-seral habitats. Annual home-range size varied from to 189 to 894 ha (x̄ =  576; SE  =  75), with little difference between breeding and nonbreeding home ranges. Breeding-season home-range size increased with the amount of hard edge, and the amount of old and mature forest combined. Core area, annual and nonbreeding season home-range sizes all increased with increased amounts of hard edge, suggesting that increased fragmentation is associated with larger core and home-range sizes. Although no effect of the amount of late-seral stage forest on either survival or home-range size was detected, these results are the first to concurrently demonstrate increased forest fragmentation with decreased survival and increased home-range size of Northern Spotted Owls.Keywords: Klamath Province, Northern Spotted Owl, habitat characteristics, Oregon, survival, home-range size, Strix occidentalis caurin