Related papers: Higher Segal spaces and partial groups
In a program to formulate and develop two-dimensional conformal field theory in the framework of algebraic geometry, Beilinson and Drinfeld have recently given a notion of ``chiral algebra'' in terms of D-modules on algebraic curves. This…
This paper investigates the projective closure of simplicial affine semigroups in $\mathbb{N}^{d}$, $d \geq 2$. We present a characterization of the Cohen-Macaulay property for the projective closure of these semigroups using Gr\"{o}bner…
In this paper we present a novel arbitrary-order discrete de Rham (DDR) complex on general polyhedral meshes based on the decomposition of polynomial spaces into ranges of vector calculus operators and complements linked to the spaces in…
We give a Quillen equivalence between model structures for simplicial operads, described via the theory of operads, and Segal operads, thought of as certain reduced dendroidal spaces. We then extend this result to give an Quillen…
Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degrees and the Cremona degrees,…
Algebra objects in $\infty$-categories of spans admit a description in terms of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects and extend this correspondence to an equivalence of $\infty$-categories.…
The purpose of this article is to present a survey of our recent results on length commensurable and isospectral locally symmetric spaces. The geometric questions led us to the notion of "weak commensurability" of two Zariski-dense…
We present the minimal realization of the $\ell$-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex Pais-Uhlenbeck oscillator equations. We introduce a minimal deformation of the…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in [N. Heuer, F. Pinochet, arXiv 1309.1697 (to appear in SIAM J. Numer. Anal.)], we study the case of a hypersingular integral…
Two theorems witnessing the abundance of geometrically trivial strongly minimal autonomous differential equations of arbitrary order are shown. The first one states that a generic algebraic vector field of degree $d\geq 2$ on the affine…
In this paper we prove characterizations of the discrete Besov spaces in terms of the heat and Poisson semigroups associated with the discrete Laplacian that will allow us to prove regularity results for the fractional powers of the…
For a commutative semi-simple Banach algebra ${A}$ which is an ideal in its second dual we give a necessary and sufficient condition for an essential abstract Segal algebra in ${A}$ to be a BSE-algebra. We show that a large class of…
In several elementary particle scenarios, self-dual fields emerge as fundamental degrees of freedom. Some examples are the $D = 2$ chiral boson, $D = 10$ Type IIB supergravity, and $D = 6$ chiral tensor multiplet theory. For those models, a…
In this paper we introduce the notion of coalgebra symmetry for discrete systems. With this concept we prove that all discrete radially symmetric systems in standard form are quasi-integrable and that all variational discrete quasi-radially…
We classify the simple modules for the rational Cherednik algebra that are irreducible when restricted to W, in the case when W is a finite Weyl group. The classification turns out to be closely related to the cuspidal two-sided cells in…
We define a category parameterizing Calabi-Yau algebra objects in an infinity category of spans. Using this category, we prove that there are equivalences of infinity categories relating, firstly: 2-Segal simplicial objects in C to algebra…
The special Galilean group, usually denoted SGal(3), is a 10-dimensional Lie group whose important subgroups include the special orthogonal group, the special Euclidean group, and the group of extended poses. We briefly describe SGal(3) and…
We show that the set of $m \times m$ complex skew-symmetric matrix polynomials of odd grade $d$, i.e., of degree at most $d$, and (normal) rank at most $2r$ is the closure of the single set of matrix polynomials with the certain, explicitly…
The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations…