Related papers: Microlocal analysis and beyond

We introduce and study the notion of a locally proper map between topological spaces. We show that fundamental constructions of sheaf theory, more precisely proper base change, projection formula, and Verdier duality, can be extended from…

We initiate the study of sheaves on Cech closure spaces, providing a new, unified approach to sheaf theory on many of the major classes of spaces of interest to applications: topological spaces, finite simplicial complexes (seen as $T_0$…

In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem~3 by Carr (1981,1983). Here we extend the theory to cover the case where the order of…

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic…

We generalize the notion of a small sheaf of sets over a topological space or manifold to define the notion of a small stack of groupoids over an \'etale topological or differentiable stack. We then provide a construction analogous to the…

This work is an introduction to the local geometric theory of Veronese webs developed in the last twenty years. Among the different possible approach, here one has chosen the point of view of differential forms. Moreover, in order to make…

Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.

The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…

We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…

Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…

Kirch topology on $\mathbb N$ goes back to 1969, and is remarkable for being Hausdorff, connected, and locally connected. In this sense, it is analogous to the usual topology on $\mathbb C,$ yet, to the author's knowledge, there have been…

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…

Benchmarking estimation and its risk evaluation is a practically important issue in small area estimation. While Bayesian methods have been widely adopted in small area estimation, existing benchmarking approaches are often ad-hoc, such as…

We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al.,…

Inspired by the geometry of wrapped Fukaya categories, we introduce the notion of wrapped microlocal sheaves. We show that traditional microlocal sheaves are equivalent to functionals on wrapped microlocal sheaves, in analogy with the…

We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…

This paper is the second part of arXiv:0707.1766. We develope harmonic analysis in some categories of filtered abelian groups and vector spaces over the fields R or C. These categories contain as objects local fields and adelic spaces…

We start with elementary algebraic theory of factorization of linear ordinary differential equations developed in the period 1880-1930. After exposing these classical results we sketch more sophisticated algorithmic approaches developed in…

This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…

Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…