KTH/SU Mathematics Colloquium
07-02-14
Andreas Strömbergsson, KTH
Some connections between number theory and dynamical systems
I will give several examples where dynamical systems play a central
role in number theoretical results, and vice versa. In particular I
will describe Ratner's theorem on equidistribution of unipotent flows
on homogeneous spaces, which has found applications in several number
theoretical problems. I will also discuss how, conversely, number
theory can be used to strengthen Ratner's theorem so that it gives an
explicit rate of convergence, in certain special cases.