Press Releases

Positive Geometry – Millions in Funding for UNIVERSE+ Project

Published Oct 26, 2023

The European Research Council (ERC) has awarded a 10 million Euro Synergy Grant to the project “UNIVERSE+: Positive Geometry in Particle Physics and Cosmology”, led by a collaborative team with Max Planck directors Johannes Henn from the Max Planck Institute for Physics in Munich and Bernd Sturmfels from the Max Planck Institute for Mathematics in the Sciences in Leipzig.

“Our team aims to create a new mathematical language,” says Johannes Henn, the project's coordinating principal investigator. “The goal is to describe physical phenomena at all scales, from the interactions of elementary particles to the large-scale structure of the universe.” Spacetime and quantum mechanics lie at the heart of physics and have led to a spectacularly successful understanding of the laws of nature. However, these pillars of fundamental physics are expected to be only approximate notions that ultimately must arise from more basic concepts. This is seen most dramatically at the Big Bang singularity, where the notion of smooth spacetime breaks down.

Associated to all scattering processes (left) and cosmological correlations (right) is a positive geometry (middle)

Hidden Geometry of Physical Laws

Recently, novel geometric shapes called “positive geometries” were discovered in the data describing the scattering of elementary particles and the correlated positions of cosmological structures in the sky. “We believe that these positive geometries have caught the tiger by the tail,” says Nima Arkani-Hamed, “giving us the first concrete examples of the way in which the principles of space-time and quantum mechanics can arise from more basic mathematical principles.” So far, however, these positive geometries have only been found in simplified toy models of the physical world. The aim of the UNIVERSE+ collaboration is to fully understand and expose these new ideas, and to find the geometries relevant to the real world, including gravity and the expanding universe.

These developments in physics are closely tied to significant advances in mathematics. “Positive geometries are fascinating objects in their own right, independent of the physical settings in which they were discovered,” says Bernd Sturmfels. “I believe that Positive Geometry has a very bright future with great potential to become a vibrant new field at the interface of physics and mathematics. To achieve this requires a coordinated effort by physicists and mathematicians in the years to come, which has now received a significant boost by the ERC Synergy Grant for the UNIVERSE+ Collaboration.”

The Team

The project UNIVERSE+ is led by Nima Arkani-Hamed (IAS Institute for Advanced Studies, Princeton), Daniel Baumann (University of Amsterdam), Johannes Henn (Max Planck Institute for Physics, Munich) and Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences, Leipzig). The Principal Investigators bring together complementary expertise in particle physics, cosmology and mathematics. This is the first collaboration of its kind, made possible by a recent confluence of critical insights in both mathematics and physics.

The group aims to attract some of the brightest young people from diverse backgrounds to work on a multi-faceted research program with the potential for significant impact on a wide range of scientific topics in particle physics, cosmology, and outward-looking mathematics. They will soon be advertising positions for researchers to join the team.

The kick-off workshop for the project is planned for February 12-16, 2024 at the Max Planck Institute for Mathematics in the Sciences in Leipzig.

ERC Synergy Grants

The ERC Synergy Grants fund collaborative projects which, due to their complexity, are carried out by several scientists and their groups in order to achieve breakthroughs that would not be possible in individual projects. To this end, the ERC provides grants of up to 10 million euros over a period of six years.