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We study finite foldable cubical complexes of nonpositive curvature (in the sense of A.D. Alexandrov). We show that such a complex X admits a graph of spaces decomposition. It is also shown that when dim X=3, X contains a closed rank one…

We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of $d$-cluster tilting modules over $d$-representation-finite algebras. This is an application of…

In \cite{LaLuRa13}, the authors completely classified the topological structure of so called {\it fractal square} $F$ defined by $F=(F+{\mathcal D})/n$, where ${\mathcal{D}}\subsetneq\{0,1,\dots,n-1\}^2, n\ge 2$. In this paper, we further…

In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset $P$ of $\{0,1\}^\NN$ there is a SFT $X$…

Let X be a complex algebraic variety, and L(X) be the scheme of formal arcs in X. Let f be an arc whose image is not contained in the singularities of X. We show that the formal neighborhood of f in L(X) admits a decomposition into a…

We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs $f\colon (X,x_0)\to (X,x_0)$, where $X$ is a complex surface having $x_0$ as a normal singularity. We prove that as long as $x_0$…

Let $G$ be a group. We denote by $\nu(G)$ an extension of the non-abelian tensor square $G \otimes G$ by $G \times G$. We prove that if $G$ is finite-by-nilpotent, then the non-abelian tensor square $G \otimes G$ is finite-by-nilpotent.…

We investigate the modularity of three non-rigid Calabi-Yau threefolds with bad reduction at 11 which arise as fibre products of rational elliptic surfaces. For this purpose, we apply a method by Serre to compare two-dimensional 2-adic…

We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory. Thus these results are for example valid over arbitrary…

We characterize the class of homotopy pull-back squares by means of elementary closure properties. The so called Puppe theorem which identifies the homotopy fiber of certain maps constructed as homotopy colimits is a straightforward…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation preserving homeomorphisms of the unit interval with finitely many breaks in slope, and also subgroups of Thompson's group F. We find geometric criteria…

The main scalar-mean extremality and rigidity results in the existing literature concern manifolds whose curvature operators are nonnegative, or warped product spaces with a log-concave warping function whose leaves carry metrics of…

We show that the right ideal of a Novikov algebra generated by the square of a right nilpotent subalgebra is nilpotent. We also prove that a $G$-graded Novikov algebra $N$ over a field $K$ with solvable $0$-component $N_0$ is solvable,…

The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…

Over a smooth complex projective curve, we study an algebraic versal deformation space with fixed determinant of a coherent sheaf. The algebraic versal deformation space decomposes into a disjoint union of Shatz strata, namely locally…

In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…

We investigate the topological nilpotence degree, in the sense of Henn-Lannes-Schwartz, of a connected Noetherian unstable algebra $R$. When $R$ is the mod $p$ cohomology ring of a compact Lie group, Kuhn showed how this invariant is…

In this paper, a new rigorous numerical method to compute fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. Decomposing the fundamental matrix solutions $\Phi(t)$ by their…

In this paper, we consider the problem of reconstructing piece-wise smooth functions from their non-uniform Fourier data. We first extend the filter method for uniform Fourier data to the non-uniform setting by using the techniques of…