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O.V. Schwarzman

Arithmetic groups (Spring 1997)

• Algebraic groups and Lie groups(background)
• Arithmetic group -what is it?
• Cofinite and cocompact arithmetic subgroups. Constructions and examples.
• The Tamagava measure and local calculations in SL(2).
• Covolumes of the arithmetic subgroups in SL(2) (Borel Theorem).
• Congruence-subgroups and the congruence problem in SL(2)(Serre theorem).
• Hyperbolic 3- orbifolds and arithmetic groups in SL(2).