Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Project B1

Asymptotic distributions, lattices and groups


Principal Investigator(s) Other Investigators
Kai-Uwe Bux
Friedrich Götze
Herbert Abels
Paul Buterus
Gennadiy P. Chistyakov
Guido Elsner
Dawid Kielak
Yuri Santos Rego
Arthur Sinulis
Martin Venker
Stefan Witzel

Summary:

In this project F. Götze will study the distribution of definite as well as indefinite forms of second and higher order on lattices in connection with lattice point problems, diophantine inequalities and the so-called quantum chaos problem. The methods developed here apply as well to approximation results for nonlinear statistics of random variables in probability theory. The investigation of indefinite forms leads to dynamical and geometric problems for linear algebraic groups as well as for their arithmetic and geometrically relevant discrete subgroups and the corresponding homogeneous spaces which will be studied by H. Abels. Here the focus is on problems by Auslander, Milnor and Siegel and the geometry of reductive groups. Joint research efforts will be devoted to the study of generic and stochastic distribution properties of eigenvectors as well as to open problems related to effective bounds for the quantitative Oppenheim-conjecture. Several of the research topics mentioned will be studied in collaboration with G.A. Margulis.

Recent Preprints:

17005 Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability PDF | PS.GZ
16054 On algebraic integers in short intervals and near smooth curves PDF | PS.GZ
16053 On points with algebraically conjugate coordinates close to smooth curves PDF | PS.GZ
16052 On distribution of points with algebraically conjugate coordinates in neighborhood of smooth curves PDF | PS.GZ
16051 Stability of Cramer’s characterization of normal laws in information distances PDF | PS.GZ
16050 Correlations between real and complex zeros of a random polynomial PDF | PS.GZ
16046 New applications of Arak’s inequalities to the Littlewood–Offord problem PDF | PS.GZ
16035 On a phenomenon discovered by Heinz Helling PDF | PS.GZ
15081 Second order concentration on the sphere PDF | PS.GZ
15080 Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law PDF | PS.GZ