Related papers: Weighted integral formulas on manifolds

The Coleman integral is a $p$-adic line integral that plays a key role in computing several important invariants in arithmetic geometry. We give an algorithm for explicit Coleman integration on curves, using the algorithms of the second…

This is a companion paper to our previous one, Avatars of Stein's Theorem in the complex setting. In this previous paper, we gave a sufficient condition for an integrable function in the upper-half plane to have an integrable Bergman…

In [GT], Goldin and the second author extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99] and [Kn08].) The main goal…

We consider a toy model of a 3-dimensional topological quantum gravity. In this model, a contribution of a given 3-manifold is given by the partition function of an abelian Topological Quantum Field Theory (TQFT), with a topological…

For an elliptic curve over Q of analytic rank 1, we use the level-two Selmer variety and secondary cohomology products to find explicit analytic defining equations for global integral points inside the set of p-adic points.

Consider the configuration spaces of manifolds. We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unordered configuration spaces of manifolds with non-trivial…

In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can obtain an analogue of the famous Stein-Weiss theorem for weighted $L^{p}$ spaces. We…

We show how the families Seiberg-Witten invariants of a family of smooth $4$-manifolds can be recovered from the families Bauer-Furuta invariant via a cohomological formula. We use this formula to deduce several properties of the families…

We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks.…

The problem studied in this work is to determine the higher weight spectra of the Projective Reed-Muller codes associated to the Veronese $3$-fold $\mathcal V$ in $PG(9,q)$, which is the image of the quadratic Veronese embedding of…

We propose a practical recipe to compute the ${s}$-parametrized maps for systems with $SU(1,1)$ symmetry using a connection between the ${Q}$ and ${P} $ symbols through the action of an operator invariant under the group. The particular…

We consider topological twists of four-dimensional $\mathcal{N}=2$ supersymmetric QCD with gauge group SU(2) and $N_f\leq 3$ fundamental hypermultiplets. The twists are labelled by a choice of background fluxes for the flavour group, which…

We discuss Poisson structures on a weighted polynomial algebra $A:=\Bbbk[x, y, z]$ defined by a homogeneous element $\Omega\in A$, called a potential. We start with classifying potentials $\Omega$ of degree deg$(x)+$deg$(y)+$deg$(z)$ with…

It is shown that for a class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichm\"uller TQFT, the Boltzmann weight assigned to a tetrahedron solves the tetrahedron equation. The dihedral angles of…

Consider a holomorphic vector bundle $L\to X$ and an open cover ${\frak U}=\{U_a\colon a\in A\}$ of $X$, parametrized by a complex manifold $A$. We prove that the sheaf cohomology groups $H^q(X,L)$ can be computed from the complex…

We have written a computer program that implements Deligne's pullback and pushforward weight spectral sequences to compute the weight graded pieces of the rational cohomology of moduli spaces of pointed smooth curves (as well as curves of…

We describe the notion of a \emph{weighting} along a submanifold $N\subset M$, and explore its differential-geometric implications. This includes a detailed discussion of weighted normal bundles, weighted deformation spaces, and weighted…

Let $\mathrm{SO}^+(p,q)$ denote the identity connected component of the real orthogonal group with signature $(p,q)$. We give a complete description of the spaces of continuous and generalized translation- and $\mathrm{SO}^+(p,q)$-invariant…

In this paper, we obtain a uniform $W^{2,\varepsilon}$-estimate of solutions to the fully nonlinear uniformly elliptic equations on Riemannian manifolds with a lower bound of sectional curvature using the ABP method.

We establish a weighted simultaneous Khintchine-type theorem, both convergence and divergence, for all nondegenerate manifolds, which answers a problem posed in [Math. Ann., 337(4):769-796, 2007]. This extends the main results of [Acta…