Research

Main directions

Methods for Feynman integrals and cosmological correlators

Differential equations, canonical forms, and the function theory underlying quantum-field-theory predictions — with applications reaching from particle physics to correlators in cosmology.

Multi-loop Feynman integrals and scattering amplitudes

Precision computations for collider physics: evaluating amplitudes at high loop order, including state-of-the-art results for five- and six-particle scattering in QCD.

Positive geometry

A new area at the interface of algebraic geometry, combinatorics, and physics: geometric objects — such as the amplituhedron — that encode physical observables directly, developed within the ERC Synergy project UNIVERSE+.

The group

Our department comprises about 15–20 researchers — PhD students, postdocs, and long-term visitors. The range of topics is broad: from precision QCD computations for collider physics, through the mathematics of Feynman integrals and special functions, to positive geometry, cosmological correlators, string theory, and connections to gravitational-wave physics. An overview of the department and its members can be found on the MPP Quantum Field Theory pages. Interested in joining? See Join & collaborate.

Research highlights

• Canonical differential equations for Feynman integrals
  Feynman integrals are the basic building blocks of predictions in quantum field theory, but computing them was long a case-by-case art. This paper showed that, in a suitable basis, the integrals satisfy differential equations of a remarkably simple, "canonical" form — turning their computation into a systematic procedure. The method has become a standard tool used throughout precision collider physics. · arXiv:1304.1806, published in Phys. Rev. Lett. 110 (2013) 251601
• Bootstrapping six-gluon QCD amplitudes
  A surprise hiding in complexity: the seemingly most complicated parts of six-particle scattering amplitudes in QCD turn out to be the simplest, making it possible to "bootstrap" the answer — reconstructing it from general principles rather than brute-force computation. With S. Carrôlo, D. Chicherin, Q. Yang, Y. Zhang. · arXiv:2510.20565
• The full four-loop cusp anomalous dimension in N=4 super Yang-Mills and QCD
  The cusp anomalous dimension is a universal quantity that governs the structure of scattering processes in any gauge theory — a kind of fingerprint of the theory. This work achieved its complete computation at four-loop order, both in QCD and in maximally supersymmetric Yang-Mills theory, a long-standing benchmark in the field. With G. P. Korchemsky and B. Mistlberger. · arXiv:1911.10174, published in JHEP 04 (2020) 018
• Solvable relativistic hydrogenlike system in supersymmetric Yang-Mills theory
  The hydrogen atom is the textbook example of an exactly solvable quantum system — but relativistic bound states in quantum field theory are notoriously hard. Here we found a fully relativistic, hydrogen-like bound-state system in supersymmetric Yang-Mills theory whose spectrum can be determined exactly. With S. Caron-Huot. · arXiv:1408.0296, published in Phys. Rev. Lett. 113 (2014) 161601
• Positivity properties of scattering amplitudes
  Many building blocks of scattering amplitudes turn out to be positive — and to remain positive under taking derivatives, infinitely often ("complete monotonicity"). This unexpected mathematical property connects amplitudes to positive geometry and leads to new numerical approximation methods for Feynman integrals. With P. Raman (arXiv:2407.05755) and with S. Ditsch and P. Raman (arXiv:2512.18499) · plenary talk at IAS Princeton, June 2024 (video)

Full publication list →

Workshops organized

• Workshop on Scattering Amplitudes and Cosmology
  ICTP Trieste, April 2023
• Holonomic Techniques for Feynman Integrals
  Max Planck Institute for Physics, October 2024
• Positive Geometry in Scattering Amplitudes and Cosmological Correlators
  ICTS Bangalore, February 2025
• Symbology@15 Conference
  Max Planck Institute for Physics, December 2025
• Les Houches Doctoral Training UNIVERSE+ School: Exploring Positive Geometry
  Les Houches, April 2026

Save the date: Amplitudes 2027

Summer School, Mainz (July 19–23) · Conference, Munich (July 26–30).