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The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
Higher Derivative (HD) Field Theories can be transformed into second order equivalent theories with a direct particle interpretation. In a simple model involving abelian gauge symmetries we examine the fate of the possible gauge fixings…
We discuss recent endeavours in connecting twistor theory to higher-spin theories and the IKKT- matrix model. Starting with a brief review on higher-spin algebra hs in four-dimensional target space, we elucidate how higher-spin symmetry can…
Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS_3-gravity can be written as an SL(2,C)…
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
Using a recent strategy to encode the space of flat connections on a three-manifold with string-like defects into the space of flat connections on a so-called 2d Heegaard surface, we propose a novel way to define gauge invariant bases for…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin…
Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of the equation that corresponds to the linear variational…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
This paper develops some new analytical solutions to the $f(\mathbb{R},\mathbb{T})$ field equations through extended gravitational decoupling. For this purpose, we take spherical anisotropic configuration as a seed source and extend it to…
The three-point functions of two scalar fields $\sigma$ and the higher spin field $h^{(\ell)}$ of HS(4) on the one side and of their proposed holographic images $\alpha$ and $\mathcal{J^{(\ell)}}$ of the minimal conformal O(N) sigma model…
We reexamine the massless spectrum of a heterotic string vacuum at large radius and present two results. The first result is to construct a vector bundle $\mathcal{Q}$ and operator $\overline{\mathcal{D}}$ whose kernel amounts to…
In the realm of invertible symmetry, the topological approach based on classifying spaces dominates the classification of 't Hooft anomalies and symmetry protected topological phases. We explore the alternative algebraic approach based on…
The major obstacle preventing Feynman diagrammatic expansions from accurately solving many-fermion systems in strongly correlated regimes is the series slow convergence or divergence problem. Several techniques have been proposed to address…
Let H be a differential graded Hopf algebra over a field k. This paper gives an explicit construction of a triple cochain complex that defines the Hochschild-Cartier cohomology of H. A certain truncation of this complex is the appropriate…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
Field theories are usually quantized by performing a path integral over configurations of classical fields. This is the case both in perturbation theory and in Wilson's nonperturbative lattice field theory. D-theory is an alternative…