Related papers: Global Analytic Approach to Super Teichmueller Spa…
There is a completely natural and intimate relationship between the diffeomorphism group of the circle and the Teichm\"uller spaces of Riemann surfaces discovered by us in 1988. Such a relationship had been sought-after by physicists from…
A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of…
In this paper, we introduce the notion of a super tangent bundle of a manifold, and extend the basic notions of differential geometry such as differential forms, exterior derivation, connection, metric and divergence on manifolds that…
In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes…
We investigate a supersymmetric generalisation of topological recursion from two perspectives: algebraic and geometric. The algebraic side concerns a recursive structure encoded in modules of a super Virasoro algebra, and the geometric…
The space of the associative commutative hyper complex numbers, H_4, is a 4-dimensional metric Finsler space with the Berwald-Moor metric. It provides the possibility to construct the tensor fields on the base of the analytical functions of…
We prove that the mapping class group $\Gamma_{g,n}$ for surfaces of negative Euler characteristic has a cofinite universal space $\E$ for proper actions (the resulting quotient is a finite $CW$-complex). The approach is to construct a…
We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…
We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global…
We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell…
Motivated by known examples of global integrals which represent automorphic L-functions, this paper initiates the study of a certain two-dimensional array of global integrals attached to any reductive algebraic group, indexed by maximal…
An effective action is obtained for the $N=1$, $2D-$induced supergravity on a compact super Riemann surface (without boundary) $\hat\Sigma$ of genus $g>1$, as the general solution of the corresponding superconformal Ward identity. This is…
We generalize the classical Fisher information metric on statistical models to $L^p$-metrics on various spaces of differential forms or group of diffeomorphisms. Using this new interpretation from information geometry, we derive several new…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…
The present paper, which is partially a review, but also contains several completely new results, aims at presenting, in a unified mathematical framework, a complex and articulated lore regarding non-compact symmetric spaces, with negative…
Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…
A concrete analysis of the general properties and numerical characteristics of different atomic and nuclear shell systems and subnuclear particles is carried out on the base of the solution scheme for an introduced in part I physical graph…
We develop a theory of large scale geometry of metrisable topological groups that, in a significant number of cases, allows one to define and identify a unique quasi-isometry type intrinsic to the topological group. Moreover, this…
As a starting point for higher-dimensional patching in the Berkovich setting, we show that this technique is applicable around certain fibers of a relative Berkovich analytic curve. As a consequence, we prove a local-global principle over…