Related papers: Whitney's index formula in higher dimensions and L…
We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…
Locally convex (or nondegenerate) curves in the sphere (or projective space) have been studied for several reasons, including the study of linear ordinary differential equations. Taking Frenet frames allows us to translate such curves into…
Work is reported on finite integral representations for 2-loop massive 2-, 3- and 4-point functions, using orthogonal and parallel space variables. It is shown that this can be utilized to cover particles with arbitrary spin (tensor…
Discrete analogs of the index Whittaker transform are introduced and investigated. It involves series and integrals with respect to a second parameter of the Whittaker function $W_{\mu, {i n} }(x), \ x >0, \ \mu \in \mathbb{R}, \ n \in…
This talk reviews Feynman integrals, which are associated to elliptic curves. The talk will give an introduction into the mathematics behind them, covering the topics of elliptic curves, elliptic integrals, modular forms and the moduli…
We find bounds on the difference between the writhing number of a smooth curve, and the writhing number of a polygon inscribed within. The proof is based on an extension of Fuller's difference of writhe formula to the case of polygonal…
The aim of this paper is to study a Laplace-type operator and its fundamental solution on the characteristic plane in the Heisenberg group $\mathbb{H}^2$. We introduce a conformal version of the Laplacian and we prove that the distance…
Let $X^k_{m,n}=\Sigma^k (\mathbb R\mathbb P^m/\mathbb R\mathbb P^n)$. In this note we completely determine the values of $k,m,n$ for which the total Stiefel-Whitney class $w(\xi)=1$ for any vector bundle $\xi$ over $X^k_{m,n}$.
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
Virtual links are generalizations of classical links that can be represented by links embedded in a ``thickened'' surface $\Sigma\times I$, product of a Riemann surface of genus $h$ with an interval. In this paper, we show that virtual…
We consider the problem of counting and of listing topologically inequivalent "planar" {4-valent} maps with a single component and a given number n of vertices. This enables us to count and to tabulate immersions of a circle in a sphere…
Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…
We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…
A simple and efficient formula is proposed for varying Abelian integrals (including their periods) under variation of the generators of the classical Schottky group representing a Riemann surface.
In this paper we compute the Reidemeister torsion of a isoenergetic surface for the integrable Hamiltonian system on the four-dimensional symplectic manifold. We use the spectral sequence defined by the filtration and following Witten-Floer…
We classify globally generated vector bundles on $\mathbb{P}^1 \times \mathbb{P}^2$ with small first Chern class, i.e. $c_1= (a,b)$, $a+b \leq 3$. Our main method is to investigate the associated smooth curves to globally generated vector…
We propose an algorithm for the application of the Laplace method for the calculation of the simplest Feynman diagram with a single loop in the scalar {\phi}^3 theory. The calculation of the contribution of such a diagram to the scattering…
This paper determines which Stiefel-Whitney numbers can be defined for singular varieties compatibly with small resolutions. First an upper bound is found by identifying the F_2-vector space of Stiefel-Whitney numbers invariant under…
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian…