Related papers: Constructive Algebraic Topology

We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…

We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…

Let $A$ be a not necessarily commutative monoid with zero such that projective $A$-acts are free. This paper shows that the algebraic K-groups of $A$ can be defined using the +-construction and the Q-construction. It is shown that these two…

We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…

We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…

Consider the Deaconu-Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of the associated groupoid C*-algebra. For a…

We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…

Let $A$ be a partial *-algebra endowed with a topology $\tau$ that makes it into a locally convex topological vector space $A[\tau]$. Then $A$ is called a topological partial *-algebra if it satisfies a number of conditions, which all…

We call a real algebraic hypersurface in $(\mathbb{C}^*)^n$ simplicial if it is given by a real Laurent polynomial in $n$-variables that has exactly $n+1$ monomials with non-zero coefficients and such that the convex hull in $\mathbb{R}^n$…

Our objective in this project is three-fold, the first two covered in this paper. In tropical mathematics, as well as other mathematical theories involving semirings, when trying to formulate the tropical versions of classical algebraic…

For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.

In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power…

Join-preserving maps on the discrete time scale $\omega^+$, referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps…

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

We usually define an algebraic structure by a set, some operations defined on this set and some propositions that the algebraic structure must validate. In some cases, we can replace these propositions by an algorithm on terms constructed…

Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…

Coalgebras for analytic functors uniformly model graph-like systems where the successors of a state may admit certain symmetries. Examples of successor structure include ordered tuples, cyclic lists and multisets. Motivated by goals in…

We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form…