DMS Algebra Seminar

Speaker: Saeed Nasseh (Georgia Southern University)

Title: Connections and lifting theory of DG modules

Abstract: Lifting theory was studied by Auslander, Ding, and Solberg for modules and by Yoshino for complexes. Further progress on this theory has been made recently (in the works of Nasseh, Ono, Sather-Wagstaff, and Yoshino) in the context of differential graded (DG) homological algebra in order to obtain a clearer insight on some major problems in commutative algebra. On the other hand, the notion of connections originates from Riemannian geometry and its history goes back to the nineteenth century in the work of Christoffel. It has been studied since then by several mathematicians and physicists including Alain Connes who generalized it to the context of noncommutative differential geometry. In this talk, I will survey recent developments on the lifting theory of DG modules and describe a relationship between this theory and a DG version of the notion of connections.

This is an in-progress joint work with Maiko Ono and Yuji Yoshino.