# Research Group: Algebraic Geometry

The research here falls into the broadly understood area of Riemann-Roch theory. Riemann-Roch theory originates from the fundamental problem of computing the dimension of so-called Riemann-Roch spaces such as the vector space of global sections of a vector bundle or, more classically, the vector space of global meromorphic functions on a compact Riemann surface that satisfy certain pole and zero order conditions. The classical and celebrated Riemann-Roch theorem from the 19th century which solves the latter problem has seen vast generalisations over the past century which are central to Algebraic K-Theory, Algebraic Geometry, Arithmetic Geometry and Differential Geometry.