Related papers: Eventually linear partially complete resolutions o…

It is shown that a separable exact residually finite dimensional C*-algebra with locally finitely generated (rational) even K-homology embeds in a uniformly hyperfinite C*-algebra.

Let X be a proper CAT(0) space. A halfspace system (or cubulation) of X is a set H of open halfspaces closed under closure-complementation and such that every point in X has a neighbourhood intersecting only finitely many walls of H. Given…

We prove that the Cuntz-Pimsner algebra associated to any surjective aperiodic one-sided subshift with finitely many left special elements has finite nuclear dimension, which is especially the case for every surjective aperiodic subshift…

We present some new and recent algorithmic results concerning polynomial system solving over various rings. In particular, we present some of the best recent bounds on: (a) the complexity of calculating the complex dimension of an algebraic…

Let $\mathfrak{a}$ be an ideal of a noetherian (not necessarily local) ring $R$ and $M$ an $R$-module with $\mathrm{Supp}_RM\subseteq\mathrm{V}(\mathfrak{a})$. We show that if $\mathrm{dim}_RM\leq2$, then $M$ is $\mathfrak{a}$-cofinite if…

We determine the simplicial compleses $\Delta$ whose Stanley-Reisner ideals $I_\Delta$ have the following property: for all $n\geq 1$ the powers $I_\Delta^n$ have linear resolutions and finite length local cohomologies.

Aimed at geometric applications, we prove the homology cobordism invariance of the $L^2$-betti numbers and $L^2$-signature defects associated to the class of amenable groups lying in Strebel's class $D(R)$, which includes some interesting…

Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $M$ be a finitely generated Cohen Macaulay $A$ module. Let $G(A)=\bigoplus_{n\geq 0}\mathfrak{m}^n/\mathfrak{m}^{n+1}$ be the associated graded ring of $A$ and $G(M)=\bigoplus_{n\geq…

In this document, some structured operator approximation theoretical methods for system identification of nearly eventually periodic systems, are presented. Let $\mathbb{C}^{n\times m}$ denote the algebra of $n\times m$ complex matrices.…

It is shown that any finite-dimensional homomorphic image of an inverse limit of nilpotent not-necessarily-associative algebras over a field is nilpotent. More generally, this is true of algebras over a general commutative ring k, with…

In this article we study any 4-dimensional Riemannian manifold $(M,g)$ with harmonic curvature which admits a smooth nonzero solution $f$ to the following equation \begin{eqnarray} \label{0002bx} \nabla df = f(Rc -\frac{R}{n-1} g) + x Rc+…

Let $\mathfrak{a}$ be an ideal of a commutative noetherian (not necessarily local) ring $R$. In the case $\cd(\mathfrak{a},R)\leq 1$, we show that the subcategory of $\mathfrak{a}$-cofinite $R$-modules is abelian. Using this and the…

We develop new techniques in order to deal with Riccati-type equations, subject to a further algebraic constraint, on Riemannian manifolds $(M^3,g)$. We find that the obstruction to solve the aforementioned equation has order $4$ in the…

In the first part of the paper we answer (positively) a question raised by the first author which has to do with some sort of rigity of the tail of resolution of an ideal. Let $I$ be a homogeneous ideal in a polynomial ring over a field of…

Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology functor with field coefficients. This construction is…

Let $R$ be a local ring of characteristic $p>0$ which is $F$-finite and has perfect residue field. We compute the generalized Hilbert-Kunz invariant for certain modules over several classes of rings: hypersurfaces of finite representation…

We prove that if M, N are finite modules over a Gorenstein local ring R of codimension at most 4, then the vanishing of Ext^n_R(M,N) for n\gg 0 is equivalent to the vanishing of Ext^n_R(N,M) for n\gg 0. Furthermore, if the completion of $R$…

We apply E. Cartan's method of equivalence to classify 7-dimensional, 2-nondegenerate CR manifolds $M$ up to local CR equivalence in the case that the cubic form of $M$ satisfies a certain symmetry property with respect to the Levi form of…

We consider a general class of $N\times N$ random matrices whose entries $h_{ij}$ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous…

We study algebraic complexity classes and their complete polynomials under \emph{homogeneous linear} projections, not just under the usual affine linear projections that were originally introduced by Valiant in 1979. These reductions are…