The topic of the talk is the study of syzygies of graded
rings, more precisely homogeneous coordinate rings of algebraic
varieties. These are special graded rings where the structure of the
syzygy modules can be understood to some extent using a mixture of
algebraic and geometric methods. The guiding question is how to
guarantee that the first few syzygy modules will be as simple as
possible, a line of research started in the case at hand by Green and
Lazarsfeld thirty years ago. The concrete class of varieties we look at
are complete group varieties, the methods will range from vanishing
theorems to convex geometry (in the form of Newton-Okounkov bodies). If
time permits we will mention results of similar flavour for moduli
spaces of sheaves. This is an account of joint work with Victor Lozovanu
und Yusuf Mustopa. Speaker(s): Alex Küronya (Goethe-Universität Frankfurt)