Related papers: What is a perverse sheaf?
Let H be an arrangement of real hyperplanes in R^n. The complexification of H defines a natural stratification of C^n. We denote by Perv(C^n, H) the category of perverse sheaves on C^n smooth with respect to this stratification. We give a…
We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…
Being able to predict the length of a scientific paper may be helpful in numerous situations. This work defines the paper length prediction task as a regression problem and reports several experimental results using popular machine learning…
The geometric Satake isomorphism is an equivalence between the categories of spherical perverse sheaves on affine Grassmanian and the category of representations of the Langlands dual group. We provide a similar description for derived…
Spreadsheets (sometimes also called Excel programs) are powerful tools which play a business-critical role in many organizations. However, due to faulty spreadsheets many bad decisions have been taken in recent years. Since then, a number…
The paper reviews some of the recent progress in the understanding of anomalous scaling and intermittency in a simple hydrodynamical model. It is directed to a non-specialized audience.
We exhibit an intimate relationship between "reciprocity sheaves" from arXiv:1402.4201 [math.AG] and "modulus sheaves with transfers" from arXiv:1908.02975 [math.AG] and arXiv:1910.14534 [math.AG].
We relate the notions of BB-tilting and perverse derived equivalence at a vertex. Based on these notions, we define mutations of algebras, leading to derived equivalent ones. We present applications to endomorphism algebras of…
We extend the theory of spinor class field and representation fields previously defined for lattices over the ring of integers of a number field to both, lattices over the coordinate ring of a smooth irreducible affine curve over a finite…
This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two…
We discuss a non-intuitive situation concerning percentages.
We introduce a class of noncommutative spectra and give the sheaf structure on the class of noncommutative spectra.
A construction of the tangent dg Lie algebra of a sheaf of operad algebras on a site is presented. The requirements on the site are very mild; the requirements on the algebra are more substantial. A few applications including the…
We provide an introductory exposition to the sheaf topos theoretic description of classical field theory motivated by the rigorous description of both $\bf{(i)}$ the variational calculus of (infinite dimensional) field-theoretic spaces, and…
This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.
This paper describes a framework for a systematic classification of spreadsheet errors. This classification or taxonomy of errors is aimed at facilitating analysis and comprehension of the different types of spreadsheet errors. The taxonomy…
The notions of consistent pairs and consistent chains of t-structures are introduced. A theorem that two consistent chains of t-structures generate a distributive lattice is proven. The technique developed is then applied to the pairs of…
This survey paper discusses different forms of malicious techniques that can affect how an information retrieval model retrieves documents for a query and their remedies.
Spreadsheets are ubiquitous, heavily relied on throughout vast swathes of finance, commerce, industry, academia and Government. They are also acknowledged to be extraordinarily and unacceptably prone to error. If these two points are…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…