-
Jan Piclum (University of Siegen), Mohamed Barakat (University of Siegen), Robin Brüser (University Siegen), Tobias Huber (Siegen U)2/13/23, 2:00 PM
-
Wolfgang Hein2/13/23, 2:10 PM
February 11, 2023 marks the 100th anniversary of the death of Wilhelm Killing. Far from all scientific centers, Killing formulated a research program that is still relevant today and has significantly influenced mathematical research for a century, namely the structure theory of Lie algebras. The 100th anniversary of Killing's death is an appropriate opportunity to honour Killing's merits...
Go to contribution page -
Claude Duhr2/13/23, 3:00 PM
We argue that Yangian-invariant l-loop fishnet integrals in 2 dimensions are closely related to a family of Calabi-Yau l-folds.
Go to contribution page
This allows us to reduce the computation of these integrals to the computation of the Calabi-Yau periods. The periods are solutions of the Picard-Fuchs differential equations, which in turn are determined by the Yangian symmetry. Finally, we show that the values of... -
Stefan Weinzierl2/13/23, 4:30 PM
The method of differential equations is a popular method to compute Feynman integrals. It is particular powerful if the differential equation can be cast into an epsilon-factorised form. In this talk I will discuss how this can be achieved for Feynman integrals which are related to non-trivial geometries like Calabi-Yau manifolds.
Go to contribution page -
Andrew McLeod2/13/23, 5:30 PM
The analytic properties of Feynman integrals are heavily constrained by basic physical principles such as causality and locality; however, the specific implications of these principles remain only partially known. In this talk, I will describe two methods for deriving concrete constraints on the analytic structure of Feynman integrals. The first of these methods leverages information about the...
Go to contribution page -
Claus Fieker2/14/23, 9:00 AM
I will give a survey about interpolation, evaluation, and
Go to contribution page
reconstruction methods for multivariate polynomial and rational problems with applications in linear algebra and Groebner basis. This will include both asymptotically fast as well as practical algorithms. -
Christoph Nega2/14/23, 10:00 AM
In this talk I will explain how one can compute ice cone integrals in two dimensions for arbitrary loop order and which mathematical structures show up in this procedure. Using a leading singularity analysis we can find two copies of the banana graph which are related to period integrals on Calabi-Yau varieties. This observation allows us to express also the ice cone through iterated...
Go to contribution page -
Tiziano Peraro2/14/23, 11:15 AM
I will discuss recent progress in techniques for generating and reconstructing multi-loop scattering amplitudes. I will focus on novel developments in physical projectors, reduction to master integrals and partial fraction decomposition, as well as their combination with finite fields and rational reconstruction methods.
Go to contribution page -
Gaia Fontana2/14/23, 11:45 AM
Intersection theory allows to exploit the vector space structure obeyed by Feynman integrals, turning the decomposition to master integrals into the calculation of the projection of a vector into a basis, via scalar products called intersection numbers. In this talk I will discuss how the calculation of intersection numbers can be achieved via a purely rational algorithm, through the...
Go to contribution page -
Yang Zhang2/14/23, 2:30 PM
In this talk, we are glad to introduce two packages, pfd-parallel and NeatIBP, based on computational algebraic geometry, aiming at cutting-edge computations for multi-loop Feynman integrals. The former one, powered by Singular and the massive parallelization framework GPI/space, implements multivariate partial fraction algorithms for simplifying analytic coefficients in multi-loop...
Go to contribution page -
Janko Böhm2/14/23, 3:00 PM
In this talk, I will first discuss the Singular/GPI-Space project which aims to bring together computer algebra systems and the workflow management system GPI-Space to perform massive parallel computations. I will illustrate how GPI-Space leverages a coordination language based on the idea of Petri nets to efficiently model algorithms. Focusing on specific use cases, I will demonstrate how...
Go to contribution page -
Bakul Agarwal (KIT)2/14/23, 4:30 PM
Integration By parts Reduction to master integrals is an essential step in most modern multi-loop scattering amplitude calculations. In recent years, IBP reduction based on syzygy methods has become increasingly popular, allowing the calculation of many challenging processes. We will discuss our approach to calculate these syzygies using linear algebra and finite field based methods, as well...
Go to contribution page -
Vitaly Magerya2/14/23, 5:00 PM
I'd like to present Rational Tracer, a solver of systems of Integration-By-Parts relations (and more) based on modular arithmetic methods, and explain how using new programming ideas we can achieve lower evaluation times and higher flexibility for practical IBP solving.
Go to contribution page -
David Broadhurst2/15/23, 9:00 AM
The generic 2-loop kite integral has 5 internal masses. Its
Go to contribution page
completion by a sixth propagator gives a 3-loop tadpole
whose substructure involves 12 elliptic curves. I shall show
how to compute all such kites and their tadpoles, with 200
digit precision achieved in seconds, thanks to the procedure
of the arithmetic-geometric mean for complete elliptic
integrals of the third kind. The number... -
Daniel Juteau2/15/23, 10:00 AM
Following Francis Brown, I will explain why certain questions in number theory, like irrationality of zeta values, make it desirable to be able to compute some mixed Tate motives of moduli spaces. Then I will explain an algorithm devised by Clément Dupont in his Ph.D. thesis for that purpose, and its implementation in the package MotivesForBiarrangements, which uses CAP (Categories,...
Go to contribution page -
Ben Page2/15/23, 11:30 AM
Multi-particle scattering amplitudes beyond tree level are complicated functions of many variables. In practical computations, amplitudes are organized as a linear combination of transcendental functions with rational functions as coefficients. The computation of these rational functions in cutting-edge cases poses a significant challenge. In the modern approach, these rational functions are...
Go to contribution page -
Robin Marzucca2/15/23, 12:00 PM
I will review a recent mathematical technique to efficiently compute scattering amplitudes in the forward scattering limit of N=4 SYM and explain how it can be used to fully determine the function space of scattering amplitudes in this limit to all orders in perturbation theory.
Go to contribution page -
Antonela Matijašić2/15/23, 2:30 PM
The state–of–the–art in current two–loop QCD amplitude calculations is at five-particle scattering. In contrast, very little is known at present about two–loop six–particle scattering processes. Computing two–loop six–particle processes requires knowledge of the corresponding one–loop amplitudes to higher orders in the dimensional regulator. In this talk, I will show the analytic results for...
Go to contribution page -
Carsten Schneider2/15/23, 3:00 PM
We report on a collection of computer algebra algorithms and their implementations that have been used in recent calculations of massive and massless 3-loop Feynman integrals. Among them we will focus on symbolic summation and integration methods, (partial) linear differential and difference equation solvers and the large moment method. A specific feature of all the techniques is that the...
Go to contribution page -
Johannes Blümlein2/15/23, 4:30 PM
In this talk we will elaborate, among others, on root-valued alphabets and elliptic structures in Massive Operator Matrix Elements, together with concrete phenomenological results at O(a_s^3).
Go to contribution page -
Lance Dixon2/16/23, 9:00 AM
In planar N=4 super-Yang-Mills theory, some scattering amplitudes and form factors that evaluate to multiple polylogarithms can be bootstrapped, or constructed without knowing the precise Feynman integrals, in some cases through eight loops. This allows a window into high orders of perturbation theory for certain scattering processes. Remarkably, the 6-gluon amplitude and the 3-gluon form...
Go to contribution page -
Clément Dupont2/16/23, 10:00 AM
I will report on ongoing joint work with Francis Brown, Javier Fresán, and Matija Tapušković, in which we prove that dimensionally regularized Feynman integrals are closed under the action of the motivic Galois group, termwise in the epsilon expansion. This fits into a larger framework of motivic Galois theory for algebraic Mellin transforms, where the main protagonists are formal versions of...
Go to contribution page -
Nikolaos Syrrakos2/16/23, 11:30 AM
-
Pierpaolo Mastrolia2/16/23, 12:00 PM
Elaborating on the recent developments concerning Feynman integrals' calculus, I shall introduce Intersection Theory for twisted de Rham co-homology, and mainly discuss the impact of Intersection Numbers on the Vector-Space structure of special functions appearing in Mathematics and Physics.
Go to contribution page -
Antonela Matijašić
Choose timezone
Your profile timezone: