Related papers: On higher-order Fourier analysis in characteristic…

Continuing the formulation of finite $N$ Hilbert spaces in emergent theories we study in this work $S_{N}$ symmetric collective models. For the case of $N$ bosons in $d$ dimensions, which map to matrix models with commuting matrices, we…

We classify pointed $p^3$-dimensional Hopf algebras $H$ over any algebraically closed field $k$ of prime characteristic $p>0$. In particular, we focus on the cases when the group $G(H)$ of group-like elements is of order $p$ or $p^2$, that…

We prove a suite of results classifying holomorphic maps between configuration spaces of Riemann surfaces; we consider both the ordered and unordered setting as well as the cases of genus zero, one, and at least two. We give a complete…

Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces $H^p$ of the upper half-plane and we review how their Fredholm properties can be studied in terms…

Nilsystems are a natural generalization of rotations and arise in various contexts, including in the study of multiple ergodic averages in ergodic theory, in the structural analysis of topological dynamical systems, and in asymptotics for…

We present new examples of finite-dimensional Nichols algebras over fields of positive characteristic. The corresponding braided vector spaces are not of diagonal type, admit a realization as Yetter-Drinfeld modules over finite abelian…

The $k$-dimensional functional order property ($\text{FOP}_k$) is a combinatorial property of a $(k+1)$-partitioned formula. This notion arose in work of Terry and Wolf, which identified $\text{NFOP}_2$ as a ternary analogue of stability in…

In this paper we classify triangular semisimple and cosemisimple Hopf algebras over any algebraically closed field k. Namely, we construct, for each positive integer N, relatively prime to the characteristic of k if it is positive, a…

In this article, we continue the structural study of factor maps betweeen symbolic dynamical systems and the relative thermodynamic formalism. Here, one is studying a factor map from a shift of finite type $X$ (equipped with a potential…

We propose a mathematical framework that we call quantum, higher-order Fourier analysis. This generalizes the classical theory of higher-order Fourier analysis, which led to many advances in number theory and combinatorics. We define a…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

In this article, we give an explicit construction of the $p$-adic Fourier transform by Schneider and Teitelbaum, which allows for the investigation of the integral property. As an application, we give a certain integral basis of the space…

The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…

Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…

The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the…

We study Hopf algebras via tools from geometric invariant theory. We show that all the invariants we get can be constructed using the integrals of the Hopf algebra and its dual together with the multiplication and the comultiplication, and…

We derive sharp, explicit constants in inverse trace inequalities for polynomial functions belonging to $\mathbb{P}_p(T)$ (polynomial space with total degree $p$) that are orthogonal to the lower-order subspace $\mathbb{P}_n(T)$, $n\leq p$,…

Noncommutative K\"ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous…

We study hypergeometric functions of nilpotent operators in finite-dimensional settings, motivated by the algebraic structure of exceptional points in non-Hermitian quantum mechanics. Our starting point is the following exact result: if N…

We study a generalisation of operator spaces modelled on $L_p$ spaces, instead of Hilbert spaces, using the notion of $p$-complete boundedness, as studied by Pisier and Le Merdy. We show that the Fig\'a-Talamanca-Herz Algebras $A_p(G)$…