Related papers: The evaluation of loop amplitudes via differential…

We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…

I will present a new method for thinking about and for computing loop integrals based on differential equations. All required information is obtained by algebraic means and is encoded in a small set of simple quantities that I will…

We use mixed Hodge structures to investigate Feynman amplitudes as functions of external momenta and masses.

We present a semi-recursive method for calculating the rational parts of one-loop gravity amplitudes which utilises axial gauge diagrams to determine the non-factorising pieces of the amplitude. This method is used to compute the one-loop…

In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical…

We report on the development of tools to calculate loop integrals and amplitudes beyond one loop. In particular, we review new features of the program SecDec which can be used for the numerical evaluation of parametric integrals like…

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently…

The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with…

The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow…

We show some non-standard Poincar\'e type estimates in the biparametric setting with appropriate weights. We will derive these results using variants from classical estimates exploiting the interplay between maximal functions and fractional…

We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.

We motivate and describe a method based on fits with polynomials to test the smoothness of differential distributions. As a demonstration, we apply the method to several measurements of inclusive jet double-differential cross section in the…

We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of…

This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the…

In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes. In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level via the Loop-Tree…

We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…

We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant. The class of loops we consider can be modeled by a system of algebraic recurrence equations with constant coefficients. We turn the task of…

The formal properties of the recently derived set of linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle have been further exploited. The crossing properties are…

We review the Laporta algorithm for the reduction of scalar integrals to the master integrals and the differential equations technique for their evaluation. We discuss the use of the basis of harmonic polylogarithms for the analytical…

New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an…