Related papers: Grothendieck topologies from unique factorisation …
In a category $\mathcal{C}$ with a proper $(\mathcal{E}, \mathcal{M})$-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow…
We announce recent results on a connection between factorization statistics of polynomials over a finite field and the structure of the cohomology of configurations in $\mathbb{R}^3$ as a representation of the symmetric group. This…
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…
We give an interpretation of the semi-infinite intersection cohomology sheaf associated to a semisimple simply-connected algebraic group in terms of finite-dimensional geometry. Specifically, we describe a procedure for building…
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…
We study factorization algebras on configuration spaces of points on the curved, colored by elements of the root lattice. We show that the factorization algebra attached to Lusztig's quantum group can be obtained as a direct image of a…
We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov's…
Homotopical algebraic $D$-geometry combines aspects of homotopical algebraic geometry of Toen and Vezzosi and $D$-geometry of Beilinson and Drinfeld. It was introduced by the paper's last two authors and di Brino as a suitable framework for…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…
Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of…
The aim of this article is to illustrate, on the example of Dwork hypersurfaces, how the study of the representation of a finite group of automorphisms of a hypersurface in its etale cohomology allows to factor its zeta function.
This paper presents a framework for assigning intrinsic geometric structures to topological groups using only the data provided by their topological and algebraic structure. The geometrisation spits into small-scale and large-scale…
Based on homological algebra of Grothendieck categories of enriched functors, two models for Voevodsky's category of big motives with reasonable correspondences are given in this paper.
We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
We give new formulas for Grothendieck polynomials of two types. One type expresses any specialization of a Grothendieck polynomial in at least two sets of variables as a linear combination of products Grothendieck polynomials in each set of…
We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…