Third meeting, Tel Aviv University, 22.6.14
Schreiber building room 8
On the Mordell Gruber Spectrum
The Mordell constant of a lattice L in R^n is a geometrically defined quantity which takes values in the unit interval. The set of possible values is the so called Mordell-Gruber spectrum. Understanding of the spectrum is tightly related to the action of the diagonal group on the space of lattices. I will discuss a joint work with Barak Weiss in which we prove some statements regarding the spectrum.
Sets of bounded discrepancy for multi-dimensional irrational rotation
The equidistribution theorem for the irrational rotation of the circle may be stated by saying that the discrepancy D(S,n) := N(S,n) - n mes(S) = o(n), where S is any Riemann measurable set, and N(S,n) is the number of points falling into S among the first n points in the orbit. In was discovered that for certain special sets, the discrepancy actually remains bounded. Hecke and Kesten characterized the intervals with this property, called "bounded remainder intervals". In this talk I will discuss Hecke-Kesten phenomenon in multi-dimensional setting. This is joint work with Sigrid Grepstad.
(jointly with TAU asymptotic geometric analysis seminar)
High-dimensional interpolation and Minkowski lattices
Random analogues of the Minkowski theorem on lattice points in convex bodies
Minkowski's theorem states that a convex symmetric domain in R^n will intersect every lattice as soon as it is sufficiently large. Without the convexity assumption this is clearly false. However, one can still ask for a probabilistic statement on the measure of the set lattices missing a large set in R^n. In my talk I will discuss such analogous results on the space of lattices and other symmetric spaces.
You are cordially invited.
