Loop-the-Loop-2: Feynman calculus and its applications to gravity and particle physics

Session

Applied Mathematics for Feynman Calculus

10 Nov 2025, 10:30

4. Introduction of novel methods in multi-loop Feynman integral computation

Zihao Wu

10/11/2025, 10:30

Multi-loop Feynman integral computation has become an important topic in nowadays high energy physics. In this talk, I will introduce recent developments of computational tools including NeatIBP and Kira. I will also introduce their applications.

5. Uncovering Singularities in Feynman Integrals via Machine Learning

Yingxuan Xu

10/11/2025, 11:00

In this talk, I will present a machine-learning framework based on symbolic regression that systematically extracts the complete symbol alphabet of multi-loop Feynman integrals. Rather than relying on singularity analysis, the method directly targets the analytic structure, making it broadly applicable and highly interpretable across different families of integrals. I will begin by outlining...

6. Intersection Theory and Relative Cohomology for Feynman Integrals

Mingming Lu

10/11/2025, 11:40

In this talk, I will briefly review the application of intersection theory to Feynman integrals, covering both the non-relative case and the introduction of relative cohomology. Furthermore, relative cohomology allows the framework of intersection theory to be extended from the traditional Baikov representation to the Lee–Pomeransky representation and possibly beyond. The advantages and...

7. Feynman Integral Reductions Via Priority Function

Tong-Zhi Yang

10/11/2025, 12:10

Feynman integrals are central to scattering amplitudes and precision collider physics, yet their evaluation is often bottlenecked by the combinatorial complexity of integration-by-parts (IBP) reductions. There has been quite rapid progress in recent years, with developments such as finite field techniques, symbolic reduction rules, syzygies, intersection theory, improved seeding, and various...

8. Relative twisted cohomology in QFT and cosmology

Andrzej Pokraka

10/11/2025, 14:30

9. Two-loop integrals for top-pair production plus a W boson

Mattia Pozzoli

10/11/2025, 15:00

The associated production of a top-antitop quark pair with a W boson is one of the heaviest signatures probed at the LHC. The corresponding rates have been found to be consistently higher than the Standard Model predictions, calling for improved theoretical predictions.
In this talk I will discuss one of the main bottlenecks for the exact computation of the two-loop QCD amplitude, namely the...

10. Differential Space of Feynman Integrals

Wojciech Flieger

10/11/2025, 15:40

We present a novel algorithm for constructing differential operators with respect to external variables that annihilate Feynman-like integrals and give rise to the associated D-modules, based on Griffiths–Dwork reduction. By leveraging the Macaulay matrix method, we derive corresponding relations among partial differential operators, including systems of Pfaffian equations and Picard-Fuchs...

11. Bootstrapping Gravity with Crossing Symmetric Dispersion Relations

Celina Pasiecznik

I will discuss how to derive bounds on Wilson coefficients in gravitational effective field theories using fully crossing symmetric dispersion relations. These sum rules naturally isolate finite subsets of low-energy couplings without relying on the forward limit or specific high-energy completions. I will show how we validate our method by matching bounds computed previously for scalar...