It is an outstanding success for Prof. Dr. Ben Heuer: His research project in arithmetic geometry has been awarded one of Europe’s most prestigious research grants, an ERC Starting Grant. The European Research Council awards Starting Grants of up to 1.5 million euros each to outstanding early-career researchers with excellent and visionary project ideas. The aim is to foster scientific independence by supporting the establishment of the scientist’s own research group.
Ben Heuer conducts research in the field of arithmetic geometry, which uses geometric methods to investigate problems in number theory. The Pythagorean theorem, for example, is a concept many people will remember from their school days. It is closely related to a problem in number theory: determining which right-angled triangles have integer side lengths. Replacing the squares in the Pythagorean theorem with higher powers makes the problem of finding solutions considerably more difficult. In 1637, Pierre de Fermat stated in his famous “Last Theorem” that the equation has no solutions in positive integers. For more than 350 years, no one knew whether this was true – or, more importantly, why.
A key motivation for studying such equations is that research into these fundamental questions leads to profound insights into the hidden structures underlying numbers. These insights may later prove useful in entirely different contexts – both within mathematics and beyond, for example as the foundation for modern information technologies.
Ben Heuer recently succeeded in significantly extending such a hidden structure. He achieved a breakthrough in proving the “p-adic Simpson correspondence”, which relates certain arithmetic symmetries of an equation to geometric objects. Figuratively speaking, this correspondence bridges number theory and geometry. This bridge had previously only been established for equations whose geometry is one-dimensional. Ben Heuer succeeded in extending this bridge to higher dimensions. He developed a new mathematical framework for this purpose, building on the theory of perfectoid spaces introduced by Fields medallist Peter Scholze.
In his ERC project, Ben Heuer will investigate applications of this new bridge between the arithmetic and geometric worlds, particularly with regard to the Langlands programme. This is one of the central research programmes in modern mathematics, whose ideas already played a crucial role in the completed proof of Fermat’s Last Theorem in the 1990s.
Prof. Dr. Ben Heuer has been a professor at the Institute of Algebra, Number Theory and Discrete Mathematics at Leibniz University Hannover since 2025. He studied mathematics at Heidelberg University and the University of Cambridge and obtained his doctorate in London in 2019, followed by postdoctoral positions in Bonn and Frankfurt. Recently, he also received the 2026 Frontiers of Science Award, which recognises outstanding scientific work that significantly advances fundamental research in mathematics, theoretical physics and computer science. Ben Heuer’s research at LUH is part of the collaborative research centre (transregio) CRC 326 GAUS and the research training group RTG 2965 “From Geometry to Numbers”.
Due to the highly competitive selection process, ERC Grants are considered a hallmark of excellence in European research. Key selection criteria include the visionary quality of the research and the outstanding track records of the applicants. A total of 23 ERC-funded researchers across all career stages are currently based at LUH. A full overview of ongoing Starting, Consolidator and Advanced Grants at LUH is available here: https://www.uni-hannover.de/forschung/profil/herausragende-projekte/erc
Note to editors:
For further information, please contact Prof. Dr. Ben Heuer, Institute of Algebra, Number Theory and Discrete Mathematics (tel. 0511 762 3294, email: ben.heuer@math.uni-hannover.de).
