Related papers: Higher Algebraic Structures and General Field Theo…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically…
We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields.
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
Generalizing supertropical algebras, we present a "layered" structure, "sorted" by a semiring which permits varying ghost layers, and indicate how it is more amenable than the "standard" supertropical construction in factorizations of…
We study subfields of surreal numbers, called hyperseries fields, that are suited to be equipped with derivations and composition laws. We show how to define embeddings on hyperseries fields that commute with transfinite sums and all…
A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…
We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra.…
Homotopy algebra and its involutive generalisation plays an important role in the construction of string field theory. I will review recent progress in these applications of homotopy algebra and its relation to moduli spaces.
A new kind of graded Lie algebra (we call it $Z_{2,2}$ graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable bose subspace of the $Z_{2,2}$ graded Lie algebra and using relevant…
This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field theories is given, refining Segal's axioms for…
We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.
The Hodge theory of complex algebraic varieties is at heart a transcendental comparison of two algebraic structures. We survey the recent advances bounding this transcendence, mainly due to the introduction of o- minimal geometry as a…
By an additive structure on a hypersurface S in projective space we mean an effective action of commutative unipotent group on projective space which leaves S invariant and acts on S with an open orbit. It is known that these structures…
In this work we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here we…
The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…
This paper is the second in a series of three, the aim of which is to construct algebraic geometry over a free metabelian Lie algebra $F$. For the universal closure of free metabelian Lie algebra of finite rank $r \ge 2$ over a finite field…