Algebraic Geometry Seminar

[Ugo Bruzzo]

The Algebraic Geometry  "running"  Seminar will meet on Tuesday, April 24th,
at 4 pm in Room 136, with a talk by Ada Boralevi (SISSA).

Title: Homogeneous vector bundles, P-modules and quiver representations.

Abstract: A quiver is a directed graph. Quivers come from combinatorics, and
homogeneous vector bundles from algebraic geometry. In 1990 Bondal and
Kapranov established an equivalence of categories that links together
algebraic geometry, representation theory, and combinatorics. To any
homogeneous vector bundle on a rational homogeneous variety they
associate a finite dimensional representation of a given quiver (with
relations).

I will describe this equivalence in detail, and explain how it is an
excellent tool for computing cohomology of homogeneous bundles, which
leads to a generalization of the well-known Borel-Weil-Bott Theorem.
The talk will be as basic as possible: no previous knowledge of quiver
representations is required.

If time permits, I will then explain a conjectural link of the quiver
representations category with the Bernstein-Gelfand-Gelfand category
O, which could potentially lead to an infinite dimensional version of
the above mentioned equivalence. If people are interested, this could
constitute the subject of a second talk.

U. Bruzzo