There are strong indications from physics at both infinitesimal and cosmic distances that our current understanding of the laws of nature is only approximate, and must be replaced by deeper principles. The UNIVERSE+ project seeks a new foundation for fundamental physics, ranging from elementary particles to the Big Bang, revealing a hidden world of ideas beyond quantum mechanics and spacetime. Novel geometric objects recently discovered in theoretical physics hint at new mathematical structures. Combinatorics, algebra and geometry have been connected to particle physics and cosmology in an entirely unexpected way. Leveraging these advances, we will launch the field of Positive Geometry, as a new mathematical framework for describing the laws of physics. To this end, we bring together the necessary expertise in particle physics (Arkani-Hamed, Henn), cosmology (Baumann) and mathematics (Sturmfels). This is the first collaboration of its kind, made possible by a recent confluence of critical insights in both mathematics and physics, which are now so closely aligned as to propel us forward on a clear trajectory. Our goals are fiercely ambitious: we aim to create a new mathematical language for describing physical phenomena at all scales, from the interactions of elementary particles to the large-scale structure of the universe.

Few parts of Europe witnessed so many population shifts in a few centuries as the Carpathian Basin in 400-900 CE. In this macro-region along the middle Danube, Pannonians, Romans, Goths, Gepids, Longobards, Avars, Bulgars, Slavs, Franks and many others came and went. This is an intriguing test case for the relationship between ethnic identities constructed in texts, cultural habitus attested in the archaeological record, and genetic profiles that can now be analysed through ancient DNA. What was the impact of migrations and mobility on the population of the Carpathian Basin? Was the late antique population replaced, did it mix with the newcomers, or did its descendants only adopt new cultural styles? To what degree did biological distinctions correspond to the cultural boundaries and/or ethnonyms in the texts? If pursued with methodological caution, this case study will have implications beyond the field. HistoGenes will analyse c. 6,000 samples from graves with cutting edge scientific methods, and contextualize the interpretation of these data in their archaeological and historical setting. The rapid progress of aDNA analysis and of bio-informatics now make such an enterprise viable. However, the methods of historical interpretation have not kept pace. HistoGenes will, for the first time, unite historians, archaeologists, geneticist, anthropologists, and specialists in bio-informatics, isotope analysis and other scientific methods. Many team members have already collaborated successfully in a pilot project, which has demonstrated the feasibility of the approach and of the integrated workflow at the core of the project. A wide range of particular historical questions will be addressed from an interdisciplinary perspective, and fundamental theoretical and methodological issues can be explored. HistoGenes will not only advance our knowledge about a key period in European history, but also establish new standards for the historical interpretation of genetic data.