Related papers: The $\mathcal{S}$-cone and a primal-dual view on s…

Applying the classical Serre-Swan theorem, as this is extended to topological (non-normed) algebras, one attains a classification of elementary particles via their spin-structure. In this context, our argument is virtually based on a…

We study nonnegative and sums of squares symmetric (and even symmetric) functions of fixed degree. We can think of these as limit cones of symmetric nonnegative polynomials and symmetric sums of squares of fixed degree as the number of…

We study dual volume representations of canonical forms for positive geometries in projective spaces, expressing their rational canonical functions as Laplace transforms of measures supported on the convex dual of the semialgebraic set.…

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient…

We study maps between positive definite or positive semidefinite cones of unital $C^*$-algebras. We describe surjective maps that preserve (1) the norm of the quotient or multiplication of elements; (2) the spectrum of the quotient or…

In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by St{\o}rmer. Our method is based on a definition of an inner product in the space of linear maps between two…

We study the derived category of the moduli space $SU_C(2)$ of rank $2$ vector bundles on a smooth projective curve $C$ of genus $g\ge 2$ with trivial determinant. This generalizes the recent work by Tevelev and Torres on the case with…

In the monotone integer dualization problem, we are given two sets of vectors in an integer box such that no vector in the first set is dominated by a vector in the second. The question is to check if the two sets of vectors cover the…

The prepotential of N=2* supersymmetric theories with unitary gauge groups in an Omega-background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality…

The representation theory of a 3-dimensional Sklyanin algebra $S$ depends on its (noncommutative projective algebro-) geometric data: an elliptic curve $E$ in $\mathbb{P}^2$, and an automorphism $\sigma$ of $E$ given by translation by a…

In the smallest cases where there exist nonnegative polynomials that are not sums of squares we present a complete explanation of this distinction. The fundamental reason that the cone of sums of squares is strictly contained in the cone of…

We study the problem of computing weighted sum-of-squares (WSOS) certificates for positive polynomials over a compact semialgebraic set. Building on the theory of interior-point methods for convex optimization, we introduce the concept of…

A spherical n-gon is a bordered surface homeomorphic to a closed disk, with n distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs…

In (Davis and Papp, 2022), the authors introduced the concept of dual certificates of (weighted) sum-of-squares polynomials, which are vectors from the dual cone of weighted sums of squares (WSOS) polynomials that can be interpreted as…

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…

It is well-known that the second-order cone can be outer-approximated to an arbitrary accuracy $\epsilon$ by a polyhedral cone of compact size defined by irrational data. In this paper, we propose two rational polyhedral…

This is the 8th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. The article reviews the superconformal index. It is often simpler to calculate than instanton partition functions,…

As was detailed by Loewy and London in [Linear and Multilinear Algebra 6 (1978/79), no.~1, 83--90], the cone of polynomials that preserve the nonnegativity of matrices may play an important role in the solution to the nonnegative inverse…

For an exponentially decaying potential, analytic structure of the $s$-wave S-matrix can be determined up to the slightest detail, including position of all its poles and their residues. Beautiful hidden structures can be revealed by its…

The Z-property of a linear map with respect to a cone is an extension of the notion of Z-matrices. In a recent paper of Orlitzky (see Corollary 6.2 in M. Orlitzky. Positive and $\mathbf{Z}$-operators on closed convex cones, Electron. J…