Event № 740
Advisor: Prof. Amos Nevo
Abstract: Counting lattice points has a long history in number theory, that can be traced back to Gauss. I will introduce this subject, and its relation to questions regarding asymptotic properties of integral points in the plane. The main focus will be an arithmetic result regarding equidistribution of parameters that characterize primitive integral points. I will also present a similar result for rings of integers in C (e.g., Gaussian integers).
Both these results are achieved via counting lattice points w.r.t. the Iwasawa decomposition in certain simple rank-one Lie groups, a topic which I will discuss more generally, if time permits.