Some counting and equidistribution results in geometry of numbers

Jeudi 10 janvier 14:00-15:00 - Tal Horesh - IHES

Résumé : Geometry of numbers is the study of integer vectors and lattices in the n-dimensional space. I will discuss the equidistribution of certain parameters characterizing primitive integer vectors as their norms tend to infinity, such as their directions, the integral grids in their orthogonal hyperplanes, and the shortest solutions to their associated gcd equations. I will also discuss the equidistribution of primitive d-dimensional subgroups of the the integer lattice, Z^n.
The key idea is that these questions reduce to problems of counting SL(n,Z) points in SL(n,R), and in fact to the equidistribution of the Iwasawa components of SL(n,Z).

Lieu : Salle 2L8 (IMO, bâtiment 307)

Notes de dernières minutes : Café culturel à 13h par Jean Lécureux

Some counting and equidistribution results in geometry of numbers  Version PDF