Speaker: Nimish Shah (Ohio State)
Title: Equidistribution of stretching translates of curves on homogeneous spaces
Abstract: We consider a finite piece C of an analytic curve on a minimal expanding (abelian) horospherical subgroup of G=SL(n,R) associated to a certain diagonal element g in G. We consider the subgroup action of G on a finte volume homogeneous space X, and consider the trajectory of C from some point x in X. We want to understand algebraic conditions on C which ensure that in the limit, the translates of the curve Cx by powers of g get equidistributed in the (homogeneous) closure of the G-orbit of x. In this talk we describe some recent joint work with Lei Yang on this problem.
Such results have applications to metric properties of Diophantine approximation- namely, to show non-improvability of Dirichlet’s approximation on curves.