A Feynman integral is called "primitive" if it is superficially divergent and does not contain subdivergences. The "period" of a primitive graph is the coefficient of logarithmic energy dependence, or equivalently the simple pole in minimal subtraction. In recent work [2305.13506, 2403.16217] together with Kimia Shaban, we numerically computed the periods of 2 million Feynman integrals in...
Polylogarithms on higher-genus Riemann surfaces are necessary for systematic calculations of certain Feynman integrals and loop amplitudes in string theory. Employing the Schottky uniformization of a Riemann surface we construct higher-genus generating functions of polylogarithmic integration kernels, coinciding with the set of meromorphic differentials defined by Enriquez. This allows for...
We consider the problem of computing all the linear relations between the integrals of the
functions lying in a given holonomic D-module. We present in this poster a new integration
algorithm designed for handling multiple integrals of holonomic functions. This novel algorithm can be regarded as both an extension of Lairez’s reduction-based algorithm, which is limited to integrals of...
We investigate the D-module structure of Feynman integrals and Euler-Mellin integrals by means of Griffiths theorem. We present first applications to special mathematical functions and one-and two-loop integrals, and discuss the generation of corresponding Pfaffian equation they obey, via Macaulay matrix method.
What happens when we let artificial intelligence tackle mathematical problems? This work explores how Transformer neural networks—initially designed for language processing—can learn and perform tasks in computational Algebraic Geometry. As a result, we introduce a neural network model that approximates psi-class intersection numbers on the moduli space of curves. Through our analysis, we...
Study of correlation functions in AdS/CFT and in-in correlators in de Sitter space often requires the computation of Witten diagrams. Due to the complexity of evaluating radial integrals for these correlators, several indirect approaches have been developed to simplify computations. However, in momentum space, these methods have been limited to fields with integer spin. Here, we formulate...
I will present a method to calculate the Landau singularities of a Feynman integrals using Whitney stratifications. Whitney stratifications themselves are microlocal in nature, meaning that they naturally do not only live in the space we are stratifying but in the cotangent bundle of this space. With this in mind I introduce a microlocal (or rather distributional) framework for Feynman...
