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The European Research Council (ERC) has awarded a Synergy Grant of 10 million euros to the project “UNIVERSE+: Positive Geometry in Particle Physics and Cosmology”. UvA physicist Daniel Baumann is one of the four principal investigators of the project, together with Nima Arkani-Hamed (IAS, Princeton), Johannes Henn (MPI for Physics, Munich) and Bernd Sturmfels (MPI for Mathematics in the Sciences, Leipzig). The team aims to create a new mathematical language to describe physical phenomena on all scales, from the interactions of elementary particles to the large-scale structure of the Universe.
Positive Geometry
Associated to all scattering processes (left) and cosmological correlations (right) is a positive geometry (middle). This geometry is constructed purely from the energies and momenta of the external particles, and makes no reference to the evolution in spacetime.

Hidden Geometry of Physical Laws

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 a smooth spacetime breaks down.

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 on 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 spacetime 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 Principal Investigators of UNIVERSE+ 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.

Pictures from a recent workshop of the UNIVERSE+ Collaboration, including the four principal investigators.

About ERC Synergy Grants

The ERC Synergy Grants fund collaborative projects that, 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. For this purpose, the ERC allocates grants of up to 10 million euros for a period of six years.