Speaker: Sean Grate (ISU)
Title: Gorenstein graded Möbius algebras are Koszul
Abstract: The graded Möbius algebra of a matroid is an algebra encoding the combinatorics of the lattice of flats. In 2016, Maeno and Numata showed that the graded Möbius algebra of a matroid is Gorenstein if and only if the matroid is modular. We extend this result by showing that these algebras are also Koszul by showing that the defining ideals have a quadratic Gröbner basis. We also examine the Koszul property for graded Möbius algebras of affine geometries, showing that those of finite affine planes are Koszul using a filtration argument. This is joint work with Jason McCullough.