## Seminar series on motives and period integrals in Quantum field theory and String theory |

Francis Brown (University of Oxford), Erik Panzer (University of Oxford), Federico Zerbini (University of Oxford), Pierre Vanhove (IPhT CEA-Saclay)

Talks (titles, abstracts and slides) for the years 2017 - 2019 -- 2020 -- 2021 -- 2022 -- 2023 -- 2024 -- next talk

This is the page for the seminar series on motives and period integrals in Quantum field theory and String theory. The seminars are taking place in an hybrid form. The Zoom Meeting ID and the password, will be sent to the participants by email before the semaine via the mailing list

If you are interested in joining this seminar series you should contact the organisers.

pdf de l'exposé

We provide evidence through two loops, that rational letters of polylogarithmic Feynman integrals are captured by the Landau equations, when the latter are recast as a polynomial of the kinematic variables of the integral, known as the principal A-determinant. Focusing on one loop, we further show how to also obtain all non-rational letters with the help of Jacobi determinant identities. We verify our findings by explicitly constructing canonical differential equations and comparing with the existing literature, and finally extend the proof of the Cohen-Macauley property of one-loop integrals to a broader range of their kinematics.

pdf de l'exposé

Nowadays, perturbative calculations in quantum field theory provide a lucky combination of practical importance and mathematical depth. In this talk I will review some modern methods of multiloop calculations: parametric representations, IBP reduction, differential equations and dimensional recurrences. I will also discuss some open questions and new approaches which may be important for further development of multiloop methods.

pdf de l'exposé

I present various symbolic methods that are applied in an ongoing long term cooperation between RISC and DESY (Deutsches Elektronen-Synchrotron) to tackle massive 3-loop Feynman integrals. Special emphasis is put on computer algebra tools from symbolic summation and integration and the large moment method which is the basis to guess linear difference and differential equations for the underlying physical problem.

pdf de l'exposé

Feynman integrals are essential ingredients for the computation of higher order corrections to observables in collider experiments. Their analytic properties led long time ago to the conjecture that they belong to a generalized class of hypergeometric functions. In this talk, I will discuss the relation between Feynman integrals in parametric representation and A-hypergeometric functions, introduced in the late '80s by Gel'fand, Kapranov, and Zelevinsky (GKZ). I will give a brief review of A-hypergeometric functions and the differential equations they satisfy in order to show how Feynman integrals can be naturally understood as A-hypergeometric functions. I will then show how this knowledge provides a practical method to evaluate Feynman integrals using computational algebraic geometry and give some examples. Finally, inspired by GKZ, I will mention how differential equations can be set for full scattering amplitudes.

Hybrid talk from room VC1 in the TCC room at the Mathematical Institute of the University of Oxford and on zoom

pdf de l'exposé

I will present algebraic methods for computing singular loci of Feynman integrals as functions of kinematic parameters. I will demonstrate how our implementation of these methods can tackle challenging diagrams which were previously out of reach. Our approach applies to a more general class of integrals, called Euler integrals, which are twisted periods of very affine varieties. This is joint work with Claudia Fevola and Sebastian Mizera.