Parabolic geometry, homogeneous vector bundles and the Bernstein-Gelfand-Gelfand resolution.
| 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 |
| A. Boralevi |
| Quivers and the cohomology of homogeneous, (not nec. irreducible) vector bundles. |
| October 28 |
| A. Cap (U. of Vienna) |
| Invariant Differential operators and homomorphisms of induced
modules.
In this talk I will outline the duality between invariant differential operators on a homogeneous space and homomorphisms of certain induced modules. If the homogeneous space is a generalized flag manifold and one looks at bundles induced by irreducible representations, then the resulting induced modules are generalized Verma modules. I will discuss how the concept of infinitesimal character leads to strong restrictions on homomorphisms between such modules. |
| November 4 |
| A. Cap (U. of Vienna) |
| Introduction to BGG sequences.
In this talk, I will discuss the general construction of BGG sequences for parabolic geometries, starting from the algebraic background related to Kostant's version of the Bott-Borel-Weil theorem. If time permits, I will sketch the relation of the adjoint BGG sequence to infinitesimal automorphisms and deformations of parabolic geometries. |
| November 11, 18 |
| A. Boralevi |
| Quivers and the cohomology of homogeneous, (not nec. irreducible) vector bundles, con't. |
| November 25 |
| No seminar. (Thanksgiving.) |
| December 2 |
| J.M. Landsberg |
| (Generalized) Verma modules. |
Past Working Geometry Seminars:
Spring 2008
Fall 2007
2006-2007
2005-2006