TAMU Working Geometry Seminar Fall 2008

Working Geometry Seminar
Fall 2008
Tuesday at 2:00-3:30 pm in Milner 317

Parabolic geometry, homogeneous vector bundles and the Bernstein-Gelfand-Gelfand resolution.

The original BGG paper.
An expository Notices article by M. Eastwood.
Bernstein-Gelfand-Gelfand sequences by Cap, Slovak & Soucek (Annals).
A generalization of the Bernstein-Bernstein-Gelfand resolution by Lepowsky (J. Algebra).

August 26

J.M. Landsberg

Introduction and Overview.

September 2

C. Robles

Sheaves, sheaf cohomology, higher direct images.

September 9

J.M. Landsberg

G/P: examples and structure of the tangent space.

September 16

A. Boralevi

Homogeneous vector bundles on G/P, p-modules, examples.

September 22 & 30
(Sep 22 is a Monday. We will meet in Milner 216 from 2-3 o'clock.)

C. Robles

Affine Weyl group action & Hasse diagrams.

October 7

L. Oeding

Cohomology of irreducible homogeneous vector bundles, the Bott-Borel-Weil theorem, examples.

October 14, 21, 28

A. Boralevi

Cohomology of homogeneous, (not irreducible) vector bundles.

November 4

J.M. Landsberg

(Generalized) Verma modules.

November 11

C. Robles

Bernstein-Gelfand-Gelfand over G/P.

November 18

I. Zelenko

Bernstein-Gelfand-Gelfand over parabolic geometries.

November 25

No seminar. (Thanksgiving.)