Related papers: Shift-invariant homogeneous classes of random fiel…

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and…

The orbits of the symplectic group acting on the type A flag variety are indexed by the fixed-point-free involutions in a finite symmetric group. The cohomology classes of the closures of these orbits have polynomial representatives…

We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups.…

We give a combinatorial model for r-spin surfaces with parametrised boundary based on Novak (2015). The r-spin structure is encoded in terms of $\mathbb{Z}_r$-valued indices assigned to the edges of a polygonal decomposition. This…

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is…

We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

For a bundle of oriented closed smooth $n$-manifolds $\pi: E \to X$, the tautological class $\kappa_{\mathcal{L}_k} (E) \in H^{4k-n}(X;\mathbb{Q})$ is defined by fibre integration of the Hirzebruch class $\mathcal{L}_k (T_v E)$ of the…

Let $q$ be a power of a prime number $p$. Let $k=\mathbb{F}_{q}(t)$ be the rational function field with constant field $\mathbb{F}_{q}$. Let $K=k(\alpha)$ be an Artin-Schreier extension of $k$. In this paper, we explicitly describe the…

Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…

Let $G$ be a reductive group over a number field $F$, which is split at a finite place $\mathfrak{p}$ of $F$, and let $\pi$ be a cuspidal automorphic representation of $G$, which is cohomological with respect to the trivial coefficient…

We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex,…

We study the role of the mirabolic subgroup $P$ of $G=\mathbf{GL}_n(F)$ ($F$ a $p$-adic field) in smooth irreducible representations of $G$ that possess a non-zero invariant functional relative to a subgroup of the form $H_{k} =…

Let $\mathbb{V}$ denote an $n$-tuple of shifts of finite multiplicity, and denote by $\mathrm{Ann}(\mathbb{V})$ the ideal consisting of polynomials $p$ in $n$ complex variables such that $p(\mathbb{V})=0$. If $\mathbb{W}$ on $\mathfrak{K}$…

The class of normal subshifts includes irreducible infinite topological Markov shifts, irreducible infinite sofic shifts, synchronized systems, Dyck shifts, $\beta$-shifts, substitution minimal shifts, and so on. We will characterize…

For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alpha, where phi^n denotes the nth iterate of phi. When the…

In a previous paper, the author has established an extension of the Z-invariance property for integrable edge-interaction models of statistical mechanics, that satisfy the star-triangle relation (STR) form of the Yang-Baxter equation (YBE).…

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients: (1) An extension theorem, for extending…

We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of…

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a…