Perfects, resultatives and auxiliaries in early English

In this paper, we will argue for a novel analysis of the auxiliary alternation in Early English, its development and subsequent loss which has broader consequences for the way that auxiliary selection is looked at cross-linguistically. We will present evidence that the choice of auxiliaries accompanying past participles in Early English differed in several significant respects from that in the familiar modern European languages. Specifically, while the construction with have became a full-fledged perfect by some time in the ME period, that with be was actually a stative resultative, which it remained until it was lost. We will show that this accounts for some otherwise surprising restrictions on the distribution of BE in Early English and allows a better understanding of the spread of HAVE through late ME and EModE. Perhaps more importantly, the Early English facts also provide insight into the genesis of the kind of auxiliary selection found in German, Dutch and Italian. Our analysis of them furthermore suggests a promising strategy for explaining cross-linguistic variation in auxiliary selection in terms of variation in the syntactico-semantic structure of the perfect. In this introductory section, we will first provide some background on the historical situation we will be discussing, then we will lay out the main claims for which we will be arguing in the paper

Fukaya Categories as Categorical Morse Homology

The Fukaya category of a Weinstein manifold is an intricate symplectic invariant of high interest in mirror symmetry and geometric representation theory. This paper informally sketches how, in analogy with Morse homology, the Fukaya category might result from gluing together Fukaya categories of Weinstein cells. This can be formalized by a recollement pattern for Lagrangian branes parallel to that for constructible sheaves. Assuming this structure, we exhibit the Fukaya category as the global sections of a sheaf on the conic topology of the Weinstein manifold. This can be viewed as a symplectic analogue of the well-known algebraic and topological theories of (micro)localization

Derived moduli of complexes and derived Grassmannians

In the first part of this paper we construct a model structure for the category of filtered cochain complexes of modules over some commutative ring $R$ and explain how the classical Rees construction relates this to the usual projective model structure over cochain complexes. The second part of the paper is devoted to the study of derived moduli of sheaves: we give a new proof of the representability of the derived stack of perfect complexes over a proper scheme and then use the new model structure for filtered complexes to tackle moduli of filtered derived modules. As an application, we construct derived versions of Grassmannians and flag varieties.Comment: 54 pages, Section 2.4 significantly extended, minor corrections to the rest of the pape

Patterns of grammaticalization in African languages

The approach outlined in the present paper is based on observations made with African languages. Although the 1000-odd African languages display a remarkable extent of structural variation, there are certain structures that do not seem to occur in Africa. Thus, to our knowledge, an African language having anything that could be called an ergative case or a numeral classifier system has not been discovered so far. It may turn out that our approach can, in a modified form, be made applicable to languages outside Africa. This , however, is a possibility that has not been considered here. The present approach is based essentially on diachronic findings in that it uses observations on language evolution in order to account for structural differences between languages. Thus, it has double potential: apart from describing and explaining typological diversity it can also be material to reconstructing language history