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We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…
General invariants of a geometric mapping of a symmetric affine connection space are obtained in this paper. These invariants are generalizations of the previous obtained basic invariants (see [16]). Moreover, these invariants are related…
A general method for analytic inversion of geometric integral transforms is proposed
With a basic knowledge of cohomology theory, the background necessary to understand Hodge theory and polarization, Deligne's Mixed Hodge Structure on cohomology of complex algebraic varieties is described.
It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…
We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.
In these notes we aim at bringing together design theory and projective geometry over a ring. Both disciplines are well established, but the results on the interaction between them seem to be rare and scattered over the literature. Thus our…
In this paper, we shall generalize the theory of mixed Hodge structures due to Deligne and obtain a subcategory GMHS in the category of mixed Hodge structures such that we have Ext_{GMHS}^2(Q,-)\not=0 in general.
In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.
We prove that the Tate conjecture is invariant under Homological Projective Duality (=HPD). As an application, we prove the Tate conjecture in the new cases of linear sections of determinantal varieties, and also in the cases of complete…
This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…
We present two new constructions in the usual euclidean plane. We only deal with 'Grecian Geometry', with this phrase we mean elementary geometry in the two-dimensional space R 2 . We describe and prove two propositions about 'projections'.…
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's…
The geometry conjecture, which was posed nearly a quarter of a century ago, states that the fixed point set of the composition of projectors onto nonempty closed convex sets in Hilbert space is actually equal to the intersection of certain…
We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and…
We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called…
Given any compact Riemann surface $C$, there is a canonical meromorphic 2--form $\widehat\eta$ on $C\times C$, with pole of order two on the diagonal $\Delta\, \subset\, C\times C$, constructed in \cite{cfg}. This meromorphic 2--form…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…