Related papers: Quantifier elimination and minimality conditions i…
The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra ${\rm gr}_v(R)$ of a subring $(R,\mathfrak{m})$ of a valuation ring…
In the light front quantisation scheme initial conditions are usually provided on a single lightlike hyperplane. This, however, is insufficient to yield a unique solution of the field equations. We investigate under which additional…
Boundary conditions in relativistic QFT can be classified by deep results in the theory of braided or modular tensor categories.
The denotational semantics of the untyped lambda-calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent…
Valiant's conjecture asserts that the circuit complexity classes VP and VNP are distinct, meaning that the permanent does not admit polynomial-size algebraic circuits. As it is the case in many branches of complexity theory, the…
The only C*-algebras that admit elimination of quantifiers in continuous logic are $\mathbb{C}, \mathbb{C}^2$, $C($Cantor space$)$ and $M_2(\mathbb{C})$. We also prove that the theory of C*-algebras does not have model companion and show…
A concept of multi-valued cognitive maps is introduced in this paper. The concept expands the fuzzy one. However, all variables and weights are not linearly ordered in the concept, but are only partially-ordered. Such an ap- proach allows…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
We prove a theorem in 3-dimensional topological field theory: a Reshetikhin-Turaev theory admits a nonzero boundary theory iff it is a Turaev-Viro theory. The proof immediately implies a characterization of fusion categories in terms of…
Given a compatible vector field on a compact connected almost-complex manifold, we show in this article that the multiplicities of eigenvalues among the zero point set of this vector field have intimate relations. We highlight a special…
In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by…
We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras $R$. We prove that the indecomposable projective $R$-modules realize the…
In the example of the Schr\"odinger/KdV equation we give elementary treatment of the theory of finite-gap integration. The concept is equivalent to two kinds of Liouvillian integrability: quadrature integrability of linear differential…
We use the differentiability of the arithmetic volume function and an arithmetic Bertini type theorem to classify when one can find a closed point on the generic fiber of an arithmetic variety, whose heights with respect to some finite…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
This is a continuation to the paper [arXiv:1511.08164] in which a problem of minimizing normalized volumes over $\mathbb{Q}$-Gorenstein klt singularities was proposed. Here we consider its relation with K-semistability, which is an…
It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the category of sets. It follows that KH^op is equivalent to a…
Dimensional reductions of various higher dimensional (super)gravity theories lead to effectively two-dimensional field theories described by gravity coupled G/H nonlinear sigma-models. We show that a new set of complexified variables can be…
We intend to investigate the metalogical property of 'omitting types' for a wide variety of quantifier logics (that can also be seen as multimodal logics upon identifying existential quantifiers with modalities syntactically and…