Gregory Muller

Ph.D. (2010) Cornell University

First Position

Assistant professor at Louisiana State University

Dissertation

The Projective Geometry of Differential Operators

Advisor:

Yuri Berest

Research Area:

algebraic geometry, homological algebra, and representation theory

Abstract: This work studies the applications of non-commutative projective geometry to the ring of differential operators on a smooth complex variety, or more generally, a Lie algebroid on such a variety. Many classical results true about complex projective space have analogs which are proven, including Serre Finiteness, Serre Vanishing, Serre Duality, the Gorenstein property, the Koszulness property, and the Beilinson equivalence. Applications to the study of ideals, projective modules and the Grothedieck group are explored.