Related papers: Computing cohomology intersection numbers of GKZ h…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
We compute the Hochschild cohomology and homology of a class of quantum exterior algebras, with coefficients in twisted bimodules. As a result we obtain several interesting examples of the homological behavior of these algebras.
We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.
In these proceedings we will review recent progress in applying ideas from the mathematical framework of twisted cohomology to the study of canonical differential equations for Feynman integrals. Firstly, we will show how the intersection…
We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies inserts them in a family of connected, Hausdorff topologies…
We observe that the characteristic cycle of a D-module gives bounds for decomposition numbers of intersection cohomology complexes.
We introduce a theory of finite polynomial cohomology with coefficients in this paper. We prove several basic properties and introduce an Abel-Jacobi map with coefficients. As applications, we use such a cohomology theory to study…
A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.
Various equivariant intersection numbers on Hilbert schemes of points on the affine plane are computed, some of which are organized into tau-functions of 2-Toda hierarchies. A correspondence between the equivariant intersection on Hilbert…
This paper is an introduction to work motivated by the question "can multipartite entanglement be detected by homological algebra?" We introduce cochain complexes associated to multipartite density states whose cohomology detects…
The matrix model of topological field theory for the moduli space of p-th spin curves is extended to the case of the Lie algebra of the orthogonal group. We derive a new duality relation for the expectation values of characteristic…
In this work we present an explicit relation between the number of points on a family of algebraic curves over $\F_{q}$ and sums of values of certain hypergeometric functions over $\F_{q}$. Moreover, we show that these hypergeometric…
We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian functions and of multiple products of Hermite polynomials.
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…
In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We give various extensions of these rules, some new and…
We explain how the computation of induced crossed modules allows the computation of certain homotopy 2-types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give some…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
The cohomology of Lie (super)algebras has many important applications in mathematics and physics. It carries most fundamental ("topological") information about algebra under consideration. At present, because of the need for very tedious…
We provided two explicit formulas for the intersection cohomology (as a graded vector space with pairing) of the symplectic quotient by a circle in terms of the $S^1$ equivariant cohomology of the original symplectic manifold and the fixed…