Exploring Positive Geometries in Physics - Congratulations to Joris Koefler

Congratulations to Joris Koefler on the successful defense of his PhD on “Positive Geometries in Physics”, and on his postdoctoral position at the Institute for Advanced Study in Princeton. 

In his dissertation Joris investigated geometric structures that connect algebraic geometry with theoretical particle physics. His research combines methods from real and complex algebraic geometry to study positive geometries, in particular the amplituhedron, and their associated canonical differential forms. These structures provide a geometric framework for understanding scattering amplitudes, which encode information about particle interactions.

A central part of his thesis was the introduction of a new positive geometry, the limit amplituhedron, which captures the large-(\(n\)) limit of scattering amplitudes in \(\mathcal{N}=4\) supersymmetric Yang–Mills theory. His work also explored the use of mixed Hodge theory in the study of amplituhedra and positive geometries in cosmology.

Joris completed his bachelor's degrees in Physics in 2020 and Mathematics in 2022 at Ruhr University Bochum, where he worked with Evgeny Epelbaum and Christian Stump, respectively. In 2023, he obtained a master's degree in Mathematics from the University of Warwick under the supervision of Diane Maclagan. From 2023 to 2026, Joris pursued his PhD under the supervision of Rainer Sinn in Bernd Sturmfels' Nonlinear Algebra group at our institute.

Since September 2026, Joris has been a member of the School of Natural Sciences at the Institute for Advanced Study in Princeton, where he works under the mentorship of Nima Arkani-Hamed. His current research focuses on positive geometries and canonical forms, including their applications to cosmology and theories of gravity.

We warmly congratulate Joris on this achievement and wish him all the best for his next chapter in Princeton!