相关论文: An effective estimate on Betti numbers

Let X be a compact Riemann surface together with a finite set of marked points. We use Morse theoretic techniques to compute the Betti numbers of the parabolic U(2,1)-Higgs bundles moduli spaces over X. We give examples for one marked point…

In this paper, we use multivariate splines to investigate the volume of polytopes. We first present an explicit formula for the multivariate truncated power, which can be considered as a dual version of the famous Brion's formula for the…

We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a…

We uncover a connection between two seemingly separate subjects in integrable models: the representation theory of the affine Temperley-Lieb algebra, and the algebraic structure of solutions to the Bethe equations of the XXZ spin chain. We…

We make a theoretical study of $\pi\pi$ scattering with quantum numbers $J^{PC}=1^{--}$ in a finite box. To calculate physical observables for infinite volume from lattice QCD, the finite box dependence of the potentials is not usually…

We point out a gap in the proof of the Davis--Januszkiewicz theorem on cohomology of small covers of simple polytopes, and give a correction to this proof. We use this theorem to compute explicitly the Betti numbers for a wide class of…

We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological…

We investigate the notion of concentration locus introduced in \cite{CacUrs22}, in the case of Riemann manifolds sequences and its relationship with the volume of tubes. After providing a general formula for the volume of a tube around a…

We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete…

In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we prove Liouville theorems for ancient solutions satisfying the…

In this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite. This extends the recent…

We prove effective equidistribution, with polynomial rate, for large closed orbits of semisimple groups on homogeneous spaces, under certain technical restrictions (notably, the acting group should have finite centralizer in the ambient…

We define the equivariant degree and local degree of a proper $G$-equivariant map between smooth $G$-manifolds when $G$ is a compact Lie group and prove a local to global result. We show the local degree can be used to compute the…

It is a well known result of Gromov that all manifolds of a given dimension with positive sectional curvature are subject to a universal bound on the sum of their Betti numbers. On the other hand, there is no such bound for manifolds with…

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.

We prove an incidence result counting the $k$-rich $\delta$-tubes induced by a well-spaced set of $\delta$-atoms. Our result coincides with the bound that would be heuristically predicted by the Szemer\'edi--Trotter Theorem and holds in all…

We consider a generalized Ricci flow with a given (not necessarily closed) three-form and establish the higher derivatives estimates for compact manifolds. As an application, we prove the compactness theorem for this generalized Ricci flow.…

We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps. In…

We present a rough classification of differential forms on a Riemannian manifold, we consider definitions and properties of conformal Killing forms on a compact Riemannian manifold and define Tachibana numbers as an analog of the well known…

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction…