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Title: Differentials and differential operators

Speaker: Claudia Miller 

Affiliation: Syracuse University

Abstract:
In the first part, I will describe Kähler differentials and derivations and some of the history behind the classic Lipman-Zariski Conjecture, as well as a generalized question proposed by Graf. Together with Vassiliadou, we give a partial answer to Graf’s question for a certain class of varieties.

In the second portion, we turn our attention to higher order differential operators, finding explicit generators and free resolutions in some low orders for these for the hypersurfaces studied by Bernstein-Gel’fand-Gel’fand and Vigué. This is joint work with Diethorn, Jeffries, Packauskas, Pollitz, Rahmati, and Vassiliadou.

No specific algebraic or geometric background is required.