##
Cohomology of Lie algebras of vector fields on Riemann surfaces

**Friedrich Wagemann**

(Fields Institute)
We study the cohomology of various Lie algebras and differential graded

Lie algebras of vector fields on Riemann surfaces. Topics include the

Kodaira-Spencer differential graded Lie algebra and its relation to

deformation theory, its sub Lie algebra of smooth vector fields of

anti-holomorphic type and a 2 dimensional analogue of the Virasoro

algebra, and finally Krichever-Novikov algebras being Lie algebras
of

meromorphic vector fields with poles in a fixed set of points.

In conclusion we state some open problems.