On a Theorem of Furstenberg

A deep result of Furstenberg from 1967 states that if Γ is a lattice in a semisimple Lie group G, then there exists a measure on Γ

with finite first moment such that the corresponding harmonic measure on the Furstenberg boundary of G

is absolutely continuous. I will discuss some of the history of this result and some recent generalizations.



Institute for Advanced Study