# University of Toronto's Symplectic Geometry Seminar

March 30, 2007, 2:10pm

BA 1230

## V Balaji

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## Algebraic holonomy groups of stable bundles

**Abstract: **
If $X$ is a complex manifold and $E$ a holomorphic vector=20
bundle, then usually there are no holomorphic connections on $E$.
One can, nonetheless, define a close analog of the
holonomy representation in the complex setting if
$E$ is a stable vector bundle and $X$ is projective algebraic.
We define these "algebraic holonomy groups" and characterize it in=20
various ways and give some applications. (This is based on joint work with J.Kollar.)