Title: On the distribution of values of bilinear forms at tuples of integer vectors II: random quantification

Speaker: Jiyoung Han (Pusan National University)

Abstract: The famous Margulis theorem (Oppenheim conjecture) says that one can determine when the values of the given non-degenerate indefinite quadratic form at integer vectors are dense in the real line. The theorem can be extendible using Ratner’s theorem to the case of symmetric bilinear forms with $(d-1)$-tuples of integer vectors, where $d$ is the rank of the symmetric matrix associated with the given bilinear form, which is the work of Dani and Margulis.

In this talk, we will see how one can quantify their theorem randomly using Rogers’ higher moment formulas and generalize these problems to the case of symplectic forms.

Equidistribution of orbits in 2-step nilpotent translational systems and applications