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The mathematics underlying the connection between deconstruction lattices and locality diagrams of conformal models is developed from scratch, with special emphasis on classification issues. In particular, the notions of equilocality…
A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly…
We introduce a family of models incorporating random segmental substitutions and point mutations and demonstrate that such models reproduce algebraic length distributions of exact matches with the slope $-4$ observed earlier in pairwise…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
We prove that a degeneration rationally connected varieties over a field of characteristic zero always contains a geometrically irreducible subvariety which is rationally connected.
The main purpose of this paper is to study restricted formal deformations of restricted Lie-Rinehart algebras in positive characteristic $p$. For $p>2$, we discuss the deformation theory and show that deformations are controlled by the…
We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics…
In Chapter 1 we fully characterise pairs of finite graphs which form a gap in the full homomorphism order. This leads to a simple proof of the existence of generalised duality pairs. We also discuss how such results can be carried to…
In this paper we provide a new method to study global dynamics of planar quasi--homogeneous differential systems. We first prove that all planar quasi--homogeneous polynomial differential systems can be translated into homogeneous…
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular…
For an analytic family P_s of polynomials in n variables (depending on a complex number s, and defined in a neighborhood of s = 0), there is defined a monodromy transformation h of the zero level set V_s= {P_s=0} for s different from 0,…
The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…
We study orientifold projections of families of four-dimensional $\mathcal{N}=1$ toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise,…
We adapt the work of Power to describe general, not-necessarily composable, not-necessarily commutative 2-categorical pasting diagrams and their composable and commutative parts. We provide a deformation theory for pasting diagrams valued…
In using the spectral theorem of many-body Green's function theory in order to relate correlations to commutator Green's functions, it is necessary in the standard procedure to consider the anti-commutator Green's functions as well whenever…
We show that there exist a nontrivial contribution on the Witten covariant phase space when the Gauss-Bonnet topological term is added to the Dirac-Nambu Goto action describing strings, because of the geometry of deformations is modified,…
I review a particular class of physical applications of Logarithmic Conformal Field Theory in strings propagating in changing (not necessarily conformal) backgrounds, namely D-brane recoil in flat or time-dependent cosmological backgrounds.…
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A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…