Seminar 9.24.15 Zheng

Speaker: Cheng Zheng (Ohio State)

Title: Sparse equidistribution of unipotent orbits in finite-volume quotients of PSL(2,R)

Abstract: We consider the orbits {pu(n1+γ)|n ∈ N} in Γ\PSL(2,R), where Γ is a non-uniform lattice in PSL(2,R) and {u(t)} is the standard unipotent one-parameter subgroup in PSL(2, R). Under a Diophantine condition on the intial point p, we can prove that the trajectory {pu(n1+γ )|n ∈ N} is equidistributed in Γ\PSL(2, R) for small γ > 0, which generalizes a result of Venkatesh for cocompact lattices Γ.