Related papers: Rigid Differentially Closed Fields
This note is devoted, after the result of Harui, arXiv:1306.5842, to solve some natural questions for non-singular plane curves of degree $d$ over an algebraically closed field $K$ of zero characteristic.
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
We construct some extension ({\it Stable Field Theory}) of Cohomological Field Theory. The Stable Field Theory is a system of homomorphisms to some vector spaces generated by spheres and disks with punctures. It is described by a formal…
We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
We consider non-supersymmetric four-dimensional closed string theories constructed out of tensor products of N=2 minimal models. Generically such theories have closed string tachyons, but these may be removed either by choosing a…
On objects of a triangulated category with a stability condition, we construct a topology.
We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several…
In the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center…
The purpose of this paper is to give explicit descriptions for stability groups of real rigid hypersurfaces of infinite type in $\mathbb C^2$. The decompositions of infinitesimal CR automorphisms are also given.
Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. In the case of…
This paper develops a complete foundational treatment of simplicial complexes from Euclidean spaces through geometric realizations, emphasizing concrete computations, examples, and practical verification methods. Beginning with finite point…
We define and construct mixed Hodge structures on real schematic homotopy types of complex projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on…
We find the form of three-point correlation functions of traceless symmetric conserved currents of arbitrary spin in d-dimensional conformal field theory (CFT). These are fixed up to several constants by conformal symmetry and current…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions,…
In this article, we investigate a weakened version of the spectral correspondence for twisted Higgs bundles. Namely, we construct twisted Higgs bundles from a finite covering map and a vector bundle on that covering but without requiring…
We show how Boundary Conformal Field Theory deformation techniques allow for a complete characterisation of the coupling between the discrete geometry inherited uniformizing a random Regge triangulations and open string theory.
Gravitational theories with fixed background fields break diffeomorphism invariance. This breaking can be spontaneous or explicit. A brief summary of the main consequences of these types of breaking is presented.
Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a $p$-adic analogue of Borcherds' singular theta lift. The values of rigid meromorphic cocycles at…