Related papers: On flexes associated with higher-order flexible ba…

This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…

We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…

Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…

Dendroidal sets offer a formalism for the study of $\infty$-operads akin to the formalism of $\infty$-categories by means of simplicial sets. We present here an account of the current state of the theory while placing it in the context of…

We prove a result concerning formality of the pull-back of a fibration. Our approach is to use bar complexes in the category of commutative differential graded algebras. As an application, we generalize an old result of Baum and Smith.

We investigate systems of equations, involving parameters from the point of view of both control theory and computer algebra. The equations might involve linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference as…

This paper extends graphic statics by describing the forces and moments in any 3D rigid-jointed frame structure in terms of cell complexes using homology theory of algebraic topology. Graphic statics provides a highly geometric way to…

Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…

The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity constraint. We show that the defining equations are derived from…

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…

In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…

A general framework for effective theories propagating two tensor and one scalar degrees of freedom is investigated. Geometrically, it describes dynamical foliation of spacelike hypersurfaces coupled to a general background, in which the…

In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for…

The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…

We examine higher-form symmetries of quantum lattice gauge theories through the lens of homotopy theory and operator algebras. We show that in the operator-algebraic approach both higher-form symmetries and 't Hooft anomalies arise from…

Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the…

We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step towards the classification of finite dimensional irreducible modules. Motivated by known results in type A, we…

We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved…

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher-derivative action that depends both on the first and the second Frenet-Serret curvatures is considered from a geometrical perspective. We…

We study topological string theory on elliptically fibered Calabi-Yau threefolds using mirror symmetry. We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the…