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The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…

We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact…

This paper contains theory on two related topics relevant to manifolds of normally hyperbolic singularities. First, theorems on the formal and $ C^k $ normal forms for these objects are proved. Then, the theorems are applied to give…

The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds \Gamma\backslash{\Bbb H}^d and…

With a view toward a fracton theory in condensed matter, we introduce a higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector global symmetry for p$=0$ and p$=1$…

We study the problem of bounding the number of cusps of a complex hyperbolic manifold in terms of its volume. Applying algebro-geometric methods using Mumford's work on toroidal compactifications and its generalization due to N. Mok and…

We consider gauge theories from the free evolution point of view, in which initial data satisfying constraints of a theory are given. Because the constraints are compatible with the field equations they remain so. We study a model…

We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential…

We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on…

This is a survey of results on positivity of vector bundles, inspired by the Brunn-Minkowski and Pr\'ekopa theorems. Applications to complex analysis, K\"ahler geometry and algebraic geometry are also discussed.

We give a coordinate-free description of real manifolds occurring in certain four dimensional supergravity theories with antisymmetric tensor fields. The relevance of the linear multiplets in the compactification of string and five-brane…

Using canonical methods, we study the invariance properties of a bosonic $p$--brane propagating in a curved background locally diffeomorphic to $M\times G$, where $M$ is spacetime and $G$ a group manifold. The action is that of a gauged…

Topologically non-trivial gauge field configurations are an interesting aspect of non-abelian gauge theories. These become particularly important upon quantizing the theory, especially through their effect on the pseudo-scalar spectrum.…

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels…

Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a…

We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…

We analyze to all perturbative orders the properties of two possible quantum extensions of classically on-shell equivalent antisymmetric tensor gauge models in four dimensions. The first case, related to the soft breaking of a topological…

With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…

We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large…

In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on…