Joint Number theory/Geometry and Analysis seminar

Speaker: Henrik Schlichtkrull (UCPH)

Title: Asymptotic density of integer points on wavefront spherical spaces

Abstract: Given a homogeneous space Z of an algebraic real reductive group G
and an orbit D in Z of a discrete subgroup of G with cofinite volume, and given an
increasing and exhaustive family of compact subsets B_R (called balls) of Z,
one wants to determine the expected number of points from D in B_R for large R.
For the Euclidean plane Z this is the famous circle problem of Gauss.
The talk concerns the solution of this problem, including an error estimate,
for a particular family of homogeneous spaces and a geometrically defined
family of balls.