The Algebraic Combinatorics and Fundamental Physics Unit pursues a new program in which quantum observables in particle physics and cosmology arise from underlying combinatorial and geometric structures. We aim to investigate how fundamental questions in quantum field theory and related areas of string theory connect with ideas of total positivity in algebraic combinatorics.
A central focus is on scattering amplitudes in high-energy physics - notably in N=4 super Yang–Mills theory - and their links with the positive Grassmannian, the amplituhedron, and cluster algebras. We also seek to elucidate the singularities and analytic properties of scattering amplitudes and Feynman integrals, for example through Landau analysis.
Our research further intertwines with matroid theory, non-linear algebra, and areas of geometry at the interface with combinatorics, including algebraic, tropical, convex, and the emerging field of positive geometry. At the heart of the unit’s mission is building a shared language between mathematics and theoretical physics, advancing both fields together.
