Related papers: Another Method for Proving a Hypergeometric Genera…
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof.…
We define a relative version of tiling cohomology for the purpose of comparing the topology of tiling spaces when one is a factor of the other. We illustrate this with examples, and outline a method for computing the cohomology of tiling…
This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
Generalizing Krieger's finite generation theorem, we give conditions for an ergodic system to be generated by a pair of partitions, each required to be measurable with respect to a given sub-algebra, and also required to have a fixed size.
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.
We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…
We extend the theory of probability graphons, continuum representations of edge-decorated graphs arising in graph limits theory, to the 'right convergence' point of view. First of all, we generalise the notions of overlay functionals and…
There are a number of ways to procedurally generate interesting three-dimensional shapes, and a method where a cellular neural network is combined with a mesh growth algorithm is presented here. The aim is to create a shape from a genetic…
The theories of hypergeometric functions and modular forms are highly intertwined. For example, particular values of truncated hypergeometric functions and hypergeometric character sums are often congruent or equal to Fourier coefficients…
This is an expository essay about systolic geometry. It describes a central theorem in the subject and why the proof is difficult. Then it discusses different metaphors which suggest ways to approach the problem. The metaphors connect the…
The purpose of this note is to establish an isomorphism from the vector space of extensions between two modules over a vertex algebra, to an appropriate first chiral homology of one dimensional projective space with coefficients in the…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). It is written to be accessible to graduate students. Numerous open questions in…
The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
A new and easy way of deriving Gauss's Generalized Hypergeometric Theorem is presented by using the Bilateral Binomial Theorem.
A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from…
The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.
Let $R$ be a commutative noetherian ring and $f: X \to \mathrm{Spec} R$ a proper smooth morphism, of relative dimension $n$. From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map $\mathrm{Tr}_f :…