Martin Herschend: 2-hereditary algebras from hypersurfaces

This talk is based on joint work in progress with Osamu Iyama. It concerns certain graded hypersurface rings in dimension 1 and 3. By studying tilting and cluster tilting theory for graded Cohen–Macaulay modules over these rings I will show how they are connected (via derived categories) to a certain class of algebras called 2-hereditary algebras. These are finite dimensional (non-commutative) algebras of global dimension 2 that are accessible to Iyama's higher dimensional Auslander–Reiten theory. Applying this theory will enable us to explicitly describe the 2-hereditary algebras that appear in our setting using quivers with potential, thereby gaining some insight into the category of graded Cohen–Macaulay modules.