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We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to be equivariant, local, coordinate-wise monotone, and almost…
In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-R\"ussmann condition, in real-analytic non-degenerate Hamiltonian systems…
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the…
We calibrate the reverse mathematical strength of a family of extensions of Ramsey's theorem to finite colorings of certain subsets of the natural numbers of unbounded finite dimension. Specifically, we analyze the principles…
The aim of Part II is to explore the technique of invariance of tautological equations in the realm of Gromov--Witten theory. The main result is a proof of Invariance Theorem (Invariance Conjecture~1 in [14]), via the techniques from…
An unresolved conjecture by Graham Higman states that for all $n\geq 1$ the number of conjugacy classes of the group of $n \times n$ unitriangular matrices with entries in the finite field $\mathbb{F}_q$ is a polynomial in $q$. In this…
Let $(H_{\mathbf{R}}, U_t)$ be any strongly continuous orthogonal representation of $\mathbf{R}$ on a real (separable) Hilbert space $H_{\mathbf{R}}$. For any $q\in (-1,1)$, we denote by $\Gamma_q(H_{\mathbf{R}},U_t)^{\prime\prime}$ the…
In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the…
We prove the continuity and the H\"older equivalence w.r.t.\ an Euclidean distance of the value function associated with the $L^1$ cost of the control-affine system $\dot q = \drift(q)+\sum_{j=1}^m u_j f_j(q)$, satisfying the strong…
The spin-1/2 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We…
The unpredictability of chaotic nonlinear dynamics leads naturally to statistical descriptions, including probabilistic limit laws such as the central limit theorem and large deviation principle. A key tool in the Nagaev-Guivarc'h spectral…
This paper presents the axioms for a quantum Yang-Mills theory in the Minkowski spacetime. There are two routes of analytic continuation for the Schwinger functions, namely the Wightman functions and time-ordered products of field…
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…
A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix…
In this paper, we study the relationship between the representation theory of the quantum affine algebra $\mathcal{U}_q(\widehat{\mathfrak{sl}_\infty})$ of infinite rank, and that of the quantum toroidal algebra…
We prove the well-posedness of the differential equation $Au=f$ in the setting of a stratified group $\mathbb{G}$ when the considered second-order differential operator $A$ can be non-invariant and non-linear. Our approach follows the…
We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W_{1+infty} introduced by Miki. Our construction involves trivalent intertwining…
The aim of this short paper is to establish a spectral algebra analog of the Bousfield-Kan "fibration lemma" under appropriate conditions. We work in the context of algebraic structures that can be described as algebras over an operad…
We consider the matrix model of $U(N)$ refined Chern-Simons theory on $S^3$ for the unknot. We derive a $q$-difference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as…
We modify and give complete proofs for the results of Etingof-Schiffmann-Varchenko on traces of intertwiners of untwisted quantum affine algebras in the opposite coproduct and the standard grading. More precisely, we show that certain…