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Abstract:

　　The theory of scrollar syzygy resolution was introduced by Schreyer on his work for Green's conjecture for canonical curves. Besides its applications in syzygy theory,  it is also closely related to the parametrization theory of curves of small gonality and has  important applications  in the theory of Hurwitz space. However, it is still an open problem on how to determine all scrollar syzygies. In this talk, we will discuss its relations with Galois theory. We will give a (conjectural) complete description of all syzygy bundles through representation theory. This is a joint work with Wouter Castryck.