Distribution of primitive lattices and their flags
Ergodic Theory and Dynamical Systems Seminar
22nd April 2021, 2:00 pm – 3:00 pm
Online, on zoom (if interested, please email one of the organisers to gain access to the Zoom link),
Integral (or primitive) lattices in $Z^n$ are the higher dimensional analog of integral (or primitive) vectors in $Z^n$. Therefore, many counting and equidistribution problems regarding integral/primitive vectors can be generalized to integral/primitive lattices. For example, Linnik type questions concern the distribution of projections of integral points on the unit sphere; these can be generalized to questions about the distribution of the projections of rank $d$ lattices in $Z^n$ to the Grassmannian $Gr(d,n)$.
Such counting and equidistribution results will be the topic of the talk, as well as their generalizations to flags of lattices.
This is joint work with Yakov Karasik.