Related papers: There is No Composition in the Computable Reducibi…

We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory. Specifically, no nonstandard model of arithmetic has a computable quotient presentation by a…

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $BC_n$; these exist only in characteristic $2$. We also give a formula for the dimensions…

While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…

We contribute to the program of extending computable structure theory to the realm of metric structures by investigating lowness for isometric isomorphism of metric structures. We show that lowness for isomorphism coincides with lowness for…

A computable graph $\mathcal{G}$ is computably categorical relative to a degree $\mathbf{d}$ if and only if for all $\mathbf{d}$-computable copies $\mathcal{B}$ of $\mathcal{G}$, there is a $\mathbf{d}$-computable isomorphism…

We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…

We consider finite extensions of the rationals which are unramified except for at 2 and infinity. We show there are no such extensions of degrees 9 through 15.

We prove two refinements of the higher Riemann-Roch without denominators: a statement for regular closed immersions between arbitrary finite dimensional noetherian schemes, with no smoothness assumptions, and a statement for the relative…

We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.

In this paper we investigate the integrability of two-dimensional partial difference equations using the newly developed techniques of study of the degree of the iterates. We show that while for generic, nonintegrable equations, the degree…

In this note, we give a new nonexistence result of ternary extremal self-dual codes.

J. Wahl conjectured that every quasihomogeneous isolated normal singularity admits a positive grading for which there are no derivations of negative weighted degree. We confirm his conjecture for quasihomogeneous isolated complete…

We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter $\delta=2$

Let G be a simple, simply connected and connected algebraic group over an algebraically closed field of characteristic p>0, and let V be a rational G-module such that dim V <= p. According to a result of Jantzen, V is completely reducible,…

The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table…

We study a metric version of the simplicial volume on Riemannian manifolds, the Lipschitz simplicial volume, with applications to degree theorems in mind. We establish a proportionality principle and a product inequality from which we…

In this paper, we study the combinatorics of congruence subgroups of the modular group by generalizing results obtained in the non-modular case. For this, we define a notion of irreducible solutions from which we can build all the…

We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between…

We prove that there is no class-dual for almost all sublinear models on graphs.

We study the directional entropy of the dynamical system associated to a $\Z^2$ configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some…