Topics in Algebra (517-1-71)

Instructors

Yizhaq Gelander

Meeting Info

Lunt Hall 102: Mon, Wed, Fri 1:00PM - 1:50PM

Overview of class

D-modules in algebra and geometry (various operations, holonomicity, V-filtration, Bernstein-Sato polynomial, resolutions, etc.), followed by a study of connections with Hodge theory, especially the study of the Hodge filtration on D-modules of Hodge theoretic origin. In particular we will be touching on some of the aspects of the theory of mixed Hodge modules and the relationship between all of the above and notions in birational geometry (singularities of pairs, multiplier ideals, vanishing theorems), and some of the recent theory of Hodge ideals.

In terms of background, the course will gradually require more and more knowledge (again, over at least two quarters): first all sorts of algebra and a bit of manifolds, then a decent grasp of algebraic geometry, then basic Hodge theory, and finally a little birational geometry. There will be a webpage containing references, and eventually some notes.

Class Materials (Required)

No textbook required

Class Materials (Suggested)

No textbook suggested