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This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…

A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…

We prove the following result related to the inverse problem for universal deformation rings of group representations: Given a finite field k, denote by W(k) the ring of Witt vectors over k and by K the field of fractions of W(k). If a…

Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…

We consider a holomorphic 1-form $\omega$ with an isolated zero on an isolated complete intersection singularity $(V,0)$. We construct quadratic forms on an algebra of functions and on a module of differential forms associated to the pair…

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…

We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…

Finite-dimensional subalgebras of a Lie algebra of smooth vector fields on a circle, as well as piecewise-smooth global transformations of a circle on itself, are considered. A canonical forms of realizations of two- and three-dimensional…

The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to…

We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a unique conjugacy class of involutions.

In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…

The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian…

Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…

We analyze the structure of a large class of connected algebraic rings over an algebraically closed field of positive characteristic using Greenberg's perfectization functor. We then give applications to rigidity problems for…

The paper is devoted to the symmetry aspects of 2D nonlocal field theory, which is the simplest deformation of the conformally invariant quantum field theory with one free bosonic field. The inverse problem of representation theory is…

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

Following ideas of Lurie, we give in this article a general construction of equivariant elliptic cohomology without restriction to characteristic zero. Specializing to the universal elliptic curve we obtain in particular equivariant spectra…

We derive a set of recursion formulae to construct singular vectors for the $N=2$ (untwisted) algebra, by using the approach of Bauer, di Francesco, Itzykson and Zuber. Applying these formulae, we obtain explicit expressions for the charged…

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…