Related papers: Geometry of forking in simple theories

We show the existence of ($1+\frac{w_2}{w_3}$)-fast loops on semi-weighted homogeneous hypersurface singularities with weights $w_1\geq w_2>w_3$. In particular we show that semi-weighted homogeneous hypersurface singularities have metrical…

We prove a generalization of Gabrielov's rank theorem for families of rings of power series which we call W-temperate. Examples include the families of complex analytic functions and of Eisenstein series. As a Corollary, we provide rank…

The m-weak group inverse was recently studied in the literature. The purpose of this paper is to investigate new properties of this generalized inverse for ring elements. We introduce the m-weak group decomposition for a ring element and…

For any $n\geq 6$ we construct almost strongly minimal geometries of type $\bullet \overset{n}{-} \bullet \overset{n}{-}\bullet$ which are $2$-ample but not $3$-ample.

String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.

We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…

We construct examples of single-sector supersymmetry breaking based on simple deformations of supersymmetric QCD with (weakly) gauged flavor group. These theories are calculable in a weakly coupled Seiberg dual description. In these models,…

Physical and chemical properties of 2D material are highly sensitive to its structures whose regularity are seldom investigated, here we proposed a simple mechanical model whose covalent bonds are connected by angle springs, with which we…

It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the…

A class of classical affine W-algebras are shown to be isomorphic as differential algebras to the coordinate rings of double coset spaces of certain prounipotent proalgebraic groups. As an application, integrable Hamiltonian hierarchies…

We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…

In algebraic geometry specialisations and valuations play and important role. In this paper we start investigating analogous structures for Zariski structures. Specifically, we look into the existence and uniqueness properties of extensions…

We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…

We overview classifications of simple infinite-dimensional complex $\mathbb{Z}$-graded Lie (super)algebras of polynomial growth, and their deformations. A subset of such Lie (super)algebras consist of vectorial Lie (super)algebras whose…

We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be…

We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by…

We present two new constructions in the usual euclidean plane. We only deal with 'Grecian Geometry', with this phrase we mean elementary geometry in the two-dimensional space R 2 . We describe and prove two propositions about 'projections'.…

We survey recent work on the geometry and dynamics of transverse subgroups of semi-simple Lie groups.

We study geometric structures of $\mathcal{W}_4$-type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion…