Related papers: Parametrised Poincar\'e duality and equivariant fi…
We geometrically derive the explicit form of the Unitary representation of the Poincare group and use it to apply speed-of-light boosts to simple polarization basis to end up with Hawton-Baylis photon position operator with commuting…
We give an explicit description of the syntomic elliptic polylogarithm on the universal elliptic curve over the ordinary locus of the modular curve in terms of certain $p$-adic analytic moment functions associated to Katz' two-variable…
Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix…
In this paper, a simplified second-order Gaussian Poincar\'e inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a…
We establish a two-weight fractional Poincar\'e-Sobolev sandwich, consisting of a two-weight fractional Poincar\'e-Sobolev inequality and a two-weight embedding from the first-order Sobolev space to a Triebel-Lizorkin space defined via a…
It is by now well known that the Poincar\'e group acts on the Moyal plane with a twisted coproduct. Poincar\'e invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a…
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed…
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…
Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the `periodic constant' of the topological multivariable Poincar\'e series (zeta function).…
We give a new categorical approach to the Halmos-von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete…
In this paper we investigate the sensitivity analysis of parameterized nonlinear variational inequalities of second kind in a Hilbert space. The challenge of the present work is to take into account a perturbation on all the data of the…
We develop the formal theory of monads, as established by Street, in univalent foundations. This allows us to formally reason about various kinds of monads on the right level of abstraction. In particular, we define the bicategory of monads…
We present an improved version of the second order Gaussian Poincar\'e inequality, firstly introduced in Chatterjee (2009) and Nourdin, Peccati and Reinert (2009). These novel estimates are used in order to bound distributional distances…
Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including…
We propose a general approach for quantitative convergence analysis of non-reversible Markov processes, based on the concept of second-order lifts and a variational approach to hypocoercivity. To this end, we introduce the flow Poincar{\'e}…
A previously found momentum-dependent regularization ambiguity in the third post-Newtonian two point-mass Arnowitt-Deser-Misner Hamiltonian is shown to be uniquely determined by requiring global Poincar\'e invariance. The phase-space…
We develop a unified strategy to obtain the geometric logarithmic Hardy inequality on any open set M of a stratified group, provided the validity of the Hardy inequality in this setting, where the so-called "weight" is regarded to be any…
We propose a contraction of the de Sitter quantum group leading to the quantum Poincare group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non--commutative space, and the deformation parameter $q$…
We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main…
Under Poincar\'e-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on improved concentration inequalities on high-dimensional…