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Topics in Geometry and Topology (515-1-81)

Instructors

Boris L Tsygan
847/491-5598
Lunt Hall Rm 302

Meeting Info

Lunt Hall 101: Mon, Wed, Fri 2:00PM - 2:50PM

Overview of class

I will be teaching a special topics course in the fall. The time is MWF 2pm.

The course will be on various aspects of the theory of D-modules. One topic is the Riemann-Hilbert correspondence between holonomic D-modules with regular singularities and constructible sheaves, as well as more recent general case due to D'Agnolo, Schapira, and Kashiwara. A part of the course will be the theory of Ind-sheaves that is used there. I hope to put it into a more general context.

The sheaf side of the general Riemann-Hilbert correspondence, i.e. enhanced sheaves, are related to and inspired by Dima Tamarkin's sheaf theoretical microlocal construction of a category associated to the cotangent bundle of a manifold (and, more generally, to a sympplectic manifold). We will outline at least some of those connections.

We also could devote some time to D-modules in positive characteristic.

The composition of the course will depend, at least in part, on the prospective audience's feedback. Please feel free to contact me about this.

We will not have any prerequisites apart from basics of theory of rings and homological algebra. However, some parts of the exposition will probably be at the level of a seminar talk.

Class Materials (Required)

No required or suggested textbooks

Class Materials (Suggested)

No required or suggested textbooks