Related papers: Generating functions and triangulations for lectur…

We describe the cone of Hilbert functions of artinian graded modules finitely generated in degree 0 over the polynomial ring R = k[x, y] with the non-standard grading deg(x) = 1 and deg(y) = n, where n is any natural number.

This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

If $K$ and $L$ are mutually dual closed convex cones in a Hilbert space with the metric projections onto them denoted by $P_K$ and $P_L$ respectively, then the following two assertions are equivalent: (i) $P_K$ is isotone with respect to…

We introduce and provide a classification theorem for the class of Heisenberg-Fock Leibniz algebras. This category of algebras is formed by those Leibniz algebras $L$ whose corresponding Lie algebras are Heisenberg algebras $H_n$ and whose…

Given a proper cone $K$ in the Euclidean space $\mathbb{R}^n$, a square matrix $A$ is said to be $K$-semipositive if there exists an $x\in K$ such that $Ax\in \text{int}(K)$, the topological interior of $K$. The paper aims to study…

We consider the motivic Hall algebra of coherent sheaves over an irreducible reduced projective curve of arithmetic genus $1$. We introduce the composition subalgebra in the singular curve case, and show that it is isomorphic to the…

We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector…

In view of solving problems of geometric realizability of polyhedra with given geometric constraints, we describe the space of geometric realizations of a simply-connected triangulated euclidean polyhedron in $\mathbb{R}^3$ up to similarity…

We study codimension one foliations in projective space \PP^n over \CC by looking at its first order perturbations: unfoldings and deformations. We give special attention to foliations of rational and logarithmic type. For a differential…

We prove that unitary two-dimensional topological field theories are uniquely characterized by $n$ positive real numbers $\lambda _1,\ldots \lambda _n$ which can be regarded as the eigenvalues of a hermitean handle creation operator. The…

It is shown that if A is a stably finite C*-algebra and E is a countably generated Hilbert A-module, then E gives rise to a compact element of the Cuntz semigroup if and only if E is algebraically finitely generated and projective. It…

Suppose that for each n >= 0 we have a representation $M_n$ of the symmetric group S_n. Such sequences arise in a wide variety of contexts, and often exhibit uniformity in some way. We prove a number of general results along these lines in…

Let Q be a quiver. M. Reineke and A. Hubery investigated the connection between the composition monoid, as introduced by M. Reineke, and the generic composition algebra, as introduced by C. M. Ringel, specialised at q=0. In this thesis we…

In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a tour through its applications in enumerative combinatorics. Topics include geometric modeling in…

We compute the Poincare polynomial and the cohomology algebra with rational coefficeints of the manifold M_n of real points of the moduli space of algebraic curves of genus 0 with n labeled points. This cohomology is a quadratic algebra,…

This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…

The line geometric model of 3-D projective geometry has the nice property that the Lie algebra sl(4) of 3-D projective transformations is isomorphic to the bivector algebra of CL(3,3), and line geometry is closely related to the classical…

Let C(X) be the algebra generated by the curvature 2-forms of the standard hermitian line bundles over the complex homogeneous manifold X=G/B. We calculate the Hilbert polynomial of C(X) and give its presentation as a quotient of a…

In this paper, we use a branch of polyhedral geometry, Ehrhart theory, to expand our combinatorial understanding of congruences for partition functions. Ehrhart theory allows us to give a new decomposition of partitions, which in turn…