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Mathematics of Scattering Amplitudes

Project description

Unified mathematical approach to scattering amplitudes

Scattering amplitudes encode probabilities of physical processes and are used for experimental predictions in particle colliders. They also play an important role in gravitation and mathematics. Experiments demand the computation of scattering amplitudes to an unprecedented level of complexity, which requires new mathematical ideas. Funded by the European Research Council, the MaScAmp project meets this challenge by introducing a framework for the theory and calculation of scattering amplitudes while developing new concepts in algebraic geometry and theoretical physics.

Objective

MaScAmp proposes a new paradigm for fundamental interactions in physics in the form of a unified mathematical approach to scattering amplitudes. The project brings together a multidisciplinary team with expertise in pure mathematics and theoretical physics who will develop a set of novel and efficient algorithmic methods with applications in mathematics, particle physics and gravity.

Discoveries in many areas of fundamental physics depend upon a detailed understanding of the scattering of particles. Modern experiments, such as particle colliders and gravitational-wave detectors, demand high-precision theoretical computations to make new discoveries. These are deduced from physical models by a highly labour-intensive process relying on the calculation of scattering amplitudes, which assign probabilities to particle interactions. Despite a tremendous worldwide effort over many decades, the methods used to compute increasingly complex scattering amplitudes remain disparate and fragmented. The work of the PIs in distinct domains suggests unexpected symmetries and universal rules obeyed by scattering amplitudes in different-looking areas of physics. This calls for a radically new way of studying scattering amplitudes.

MaScAmp will create a unified framework for the calculation of general scattering amplitudes by building upon the latest research in mathematics, notably in algebraic geometry and number theory. As a result, MaScAmp will overcome longstanding computational bottlenecks, push the boundaries of numerous areas of theoretical physics, such as quantum field theory, gravity and string theory, and inspire new mathematical research. A widely applicable computer software implementation will enable physicists to make previously inaccessible predictions for present and future experiments. A project of MaScAmp’s scope and ambition is only achievable by combining the unique expertise of the PIs in complementary areas of mathematics and physics.

Fields of science (EuroSciVoc)

Keywords

Programme(s)

Topic(s)

Funding Scheme

HORIZON-ERC-SYG - HORIZON ERC Synergy Grants

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Call for proposal

(opens in new window) ERC-2024-SyG

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Host institution

MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Net EU contribution
€ 2 214 250,00
Address
HOFGARTENSTRASSE 8
80539 MUNCHEN
Germany
Region
Berlin Berlin Berlin
Activity type
Research Organisations
Links
Total cost
€ 2 214 250,00

Beneficiaries (4)