Ergodic theoretic methods in the context of homogeneous dynamics have been highly successful in number theoretic and other applications. A lacuna of these methods is that usually they do not give rates or effective estimates. Einseidler, Venkatesh and Margulis proved a rather remarkable quantitative equidistribution result for periodic orbits of semisimple groups in homogenous spaces that can be viewed as an effective version of a result of Mozes and Shah based on Ratner's measure classification theorem. This has been extended in more recent work of Einseidler, Venkatesh, Margulis and Mohammadi. Remarkably, the new effective results can be used to prove quantitative equidistribution results that even qualitatively where not approachable earlier.
Thu, 14/06/2018 - 16:00 to 17:15