Related papers: Using Equivariant Obstruction Theory in Combinator…
Algebraic K-theory has applications in a broad range of mathematical subjects, from number theory to functional analysis. It is also fiendishly hard to calculate. Presently there are two main inroads: motivic and cyclic homology. I've been…
We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a…
In the past decades, one of the most fruitful approaches to the study of algebraic $K$-theory has been trace methods, which construct and study trace maps from algebraic $K$-theory to topological Hochschild homology and related invariants.…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
We study some homological invariants of a given generalized bound path algebra in terms of those of the algebras used in its construction. We discuss the particular case where the algebra is a generalized path algebra and give conditions…
This paper explores topological complexity in the finite equivariant setting. We first define and study an equivariant version of Tanaka's combinatorial complexity for finite topological spaces. We explore the relationships between this…
A continous map $f: \mathbb{C}^n \rightarrow \mathbb{C}^N$ is $k$-regular if the image of any $k$ points spans a $k$-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev,…
We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
This work presents for the first time a solution to the 1821 unsolved Sawa Masayoshi's problem, giving an explicit and algebraically exact solution for the symmetric case (particular case b = c, i.e., ABC \equiv right-angled isosceles…
When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…
A mixed lattice vector space is a partially ordered vector space with two partial orderings, generalizing the notion of a Riesz space. Whereas the algebraic theory of mixed lattice structures dates back to the 1970s, the topological theory…
When a compact quantum group $H$ coacts freely on unital $C^*$-algebras $A$ and $B$, the existence of equivariant maps $A \to B$ may often be ruled out due to the incompatibility of some invariant. We examine the limitations of using…
In this article we are defining a refinement of Kool-Thomas invariants of local surfaces via the equivariant $K$-theoretic invariants proposed by Nekrasov and Okounkov. Kool and Thomas defined the reduced obstruction theory for the moduli…
We introduce a torsor-theoretic obstruction to equivariant unirationality and show that it is also sufficient for actions of finite groups on toric varieties arising from automorphisms of the torus.
Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…
Let $f_1,..., f_k:X\to N$ be maps from a complex $X$ to a compact manifold $N$, $k\ge 2$. In previous works \cite{BLM,MS}, a Lefschetz type theorem was established so that the non-vanishing of a Lefschetz type coincidence class…
The disjoint paths problem is a fundamental problem in algorithmic graph theory and combinatorial optimization. For a given graph $G$ and a set of $k$ pairs of terminals in $G$, it asks for the existence of $k$ vertex-disjoint paths…