Related papers: Differential Contracting Homotopy in Higher-Spin T…
This survey offers an overview of an on-going project on uniform symmetries in abstract stable homotopy theories. This project has calculational, foundational, and representation-theoretic aspects, and key features of this emerging field on…
In this paper, we examine the modal aspects of higher groups in Shulman's Cohesive Homotopy Type Theory. We show that every higher group sits within a modal fracture hexagon which renders it into its discrete, infinitesimal, and…
In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic…
We propose a BRST extension of the higher-spin gauge theory in $AdS_4$ with the BRST operator associated with the local Lorentz symmetry. Our construction supports manifest local Lorentz covariance and is applicable both to any homotopy…
The concepts of compact and projectively-compact spin-local spinor vertices are introduced. Vertices of this type are shown to be space-time spin-local, i.e. their restriction to any finite subset of fields is space-time local. The known…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
The Homotopy Analysis Method (HAM) is a widely used analytical approach for solving nonlinear problems, yet its theoretical foundation lacks rigorous justification, and its intrinsic correlation with perturbation theory remains ambiguous,…
We have studied free higher spin gauge fields through an investigation of their Hamiltonian dynamics. Over a flat space-time, their Hamiltonian constraints were identified and solved through the introduction of prepotentials, enjoying both…
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…
In this talk, we present some direct evidences of the Higher Spin/Vector Model correspondence. There are two particular examples we would like to address on. The first example concerns a constructive approach of four dimensional higher spin…
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…
We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…
The goal of this dissertation is to present synthetic homotopy theory in the setting of homotopy type theory. We will present various results in this framework, most notably the construction of the Atiyah-Hirzebruch and Serre spectral…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
This Thesis reviews some recent developments about higher-spin interactions in flat and constant curvature backgrounds. Particular attention is given to the ambient-space formulation of the problem, both at the cubic and at the quartic…
We study the higher derived functors of the inverse limit of a functor F: D --> Z_{(p)}-mod, where D is one of the standard categories which arise when studying the homotopy theory of the classifying space of a finite group G, e.g., the…
Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a…
We outline a program for interpreting the higher-spin dS/CFT model in terms of physics in the causal patch of a dS observer. The proposal is formulated in "elliptic" de Sitter space dS_4/Z_2, obtained by identifying antipodal points in…