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The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
This work presents some results about Wick polynomials of a vector field renormalization in locally covariant algebraic quantum field theory in curved spacetime. General vector fields are pictured as sections of natural vector bundles over…
Let $S$ be a projective simply connected complex surface and $\mathcal{L}$ be a line bundle on $S$. We study the moduli space of stable compactly supported 2-dimensional sheaves on the total spaces of $\mathcal{L}$. The moduli space admits…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
A new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical…
We study invariant systems of PDEs defining Killing vector-valued forms, and then we specialize to Killing spinor-valued forms. We give a detailed treatment of their prolongation and integrability conditions by relating the point-wise…
Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
We systematically develop a theory of stratification in the context of tensor triangular geometry and apply it to classify the localizing tensor-ideals of certain categories of spectral $G$-Mackey functors for all finite groups $G$. Our…
Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…
We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…
We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this…
The prototype of mutually independent systems are systems which are localized in spacelike separated regions. In the framework of locally covariant quantum field theory we show that the commutativity of observables in spacelike separated…
Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach,…
Let $T$ be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring and a $T$-derivation. If this derivation is continuous with respect…
We consider classes T of topological spaces (referred to as T-spaces) that are stable under continuous images and frequently under arbitrary products. A local T-space has for each point a neighborhood base consisting of subsets that are…
In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order…
We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.
The $f(R)$ theory of gravity can be expressed as a scalar tensor theory with a scalar degree of freedom $\phi$. By a conformal transformation, the action and its Gibbons-York-Hawking boundary term are written in the Einstein frame and the…
A complete classification of all zonal, continuous, and translation invariant valuations on convex bodies is established. The valuations obtained are expressed as principal value integrals with respect to the area measures. The convergence…