Tal Horesh (IST Austria)

Title: Distribution of primitive lattices and flags of lattices in Z^n
 
Abstract:
Primitive lattices in Z^n are a generalization of the concept of primitive vectors: a rank d subgroup of Z^n is called primitive if there is no other subgroup of the same rank that properly contains it. In two papers from 1998 and from 2015, Schmidt proved a counting statement for primitive lattices of any rank 1<d<n, taking into account their shapes (similarity classes modulo rotation and re-scaling, namely projections into SO(d)\SLd(R)/SLd(Z)), and directions (the subspaces that they span, namely projections into the Grassmannian GR(d,n)). We extend upon this counting statement, and also consider the shapes of the orthogonal complements of these lattices. Moreover, we introduce the concept of flags of primitive lattices, and extend this counting statement to them as well.
The meeting will be open from 14.15 (local time) for a virtual coffee with the speaker. 

Recording: https://us02web.zoom.us/rec/share/qpUwze465ijiYEGaxj6QU0kMGSHMS63-XACHTMzN5Ys40cf0Np2aMXDTTiTJlDBK.atyGHEDxX9QtapKa

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